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Jenn Leach

Jenn Leach

3 years ago

This clever Instagram marketing technique increased my sales to $30,000 per month.

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Emma Jade

Emma Jade

3 years ago

6 hacks to create content faster

Content gurus' top time-saving hacks.

6 hacks to create content faster

I'm a content strategist, writer, and graphic designer. Time is more valuable than money.

Money is always available. Even if you're poor. Ways exist.

Time is passing, and one day we'll run out.

Sorry to be morbid.

In today's digital age, you need to optimize how you create content for your organization. Here are six content creation hacks.

1. Use templates

Use templates to streamline your work whether generating video, images, or documents.

Setup can take hours. Using a free resource like Canva, you can create templates for any type of material.

This will save you hours each month.

2. Make a content calendar

You post without a plan? A content calendar solves 50% of these problems.

You can prepare, organize, and plan your material ahead of time so you're not scrambling when you remember, "Shit, it's Mother's Day!"

3. Content Batching

Batching content means creating a lot in one session. This is helpful for video content that requires a lot of setup time.

Batching monthly content saves hours. Time is a valuable resource.

When working on one type of task, it's easy to get into a flow state. This saves time.

4. Write Caption

On social media, we generally choose the image first and then the caption. Writing captions first sometimes work better, though.

Writing the captions first can allow you more creative flexibility and be easier if you're not excellent with language.

Say you want to tell your followers something interesting.

Writing a caption first is easier than choosing an image and then writing a caption to match.

Not everything works. You may have already-created content that needs captioning. When you don't know what to share, think of a concept, write the description, and then produce a video or graphic.

Cats can be skinned in several ways..

5. Repurpose

Reuse content when possible. You don't always require new stuff. In fact, you’re pretty stupid if you do #SorryNotSorry.

Repurpose old content. All those blog entries, videos, and unfinished content on your desk or hard drive.

This blog post can be turned into a social media infographic. Canva's motion graphic function can animate it. I can record a YouTube video regarding this issue for a podcast. I can make a post on each point in this blog post and turn it into an eBook or paid course.

And it doesn’t stop there.

My point is, to think outside the box and really dig deep into ways you can leverage the content you’ve already created.

6. Schedule Them

If you're still manually posting content, get help. When you batch your content, schedule it ahead of time.

Some scheduling apps are free or cheap. No excuses.

Don't publish and ghost.

Scheduling saves time by preventing you from doing it manually. But if you never engage with your audience, the algorithm won't reward your material.

Be online and engage your audience.

Content Machine

Use these six content creation hacks. They help you succeed and save time.

Michael Salim

Michael Salim

3 years ago

300 Signups, 1 Landing Page, 0 Products

I placed a link on HackerNews and got 300 signups in a week. This post explains what happened.

Product Concept

The product is DbSchemaLibrary. A library of Database Schema.

I'm not sure where this idea originated from. Very fast. Build fast, fail fast, test many ideas, and one will be a hit. I tried it. Let's try it anyway, even though it'll probably fail. I finished The Lean Startup book and wanted to use it.

Database job bores me. Important! I get drowsy working on it. Someone must do it. I remember this happening once. I needed examples at the time. Something similar to Recall (my other project) that I can copy — or at least use as a reference.

Frequently googled. Many tabs open. The results were useless. I raised my hand and agreed to construct the database myself.

It resurfaced. I decided to do something.

Due Diligence

Lean Startup emphasizes validated learning. Everything the startup does should result in learning. I may build something nobody wants otherwise. That's what happened to Recall.

So, I wrote a business plan document. This happens before I code. What am I solving? What is my proposed solution? What is the leap of faith between the problem and solution? Who would be my target audience?

My note:

Note of the exact problem and solutions I’m trying to solve

In my previous project, I did the opposite!

I wrote my expectations after reading the book's advice.

“Failure is a prerequisite to learning. The problem with the notion of shipping a product and then seeing what happens is that you are guaranteed to succeed — at seeing what happens.” — The Lean Startup book

These are successful metrics. If I don't reach them, I'll drop the idea and try another. I didn't understand numbers then. Below are guesses. But it’s a start!

Metrics I set before starting anything

I then wrote the project's What and Why. I'll use this everywhere. Before, I wrote a different pitch each time. I thought certain words would be better. I felt the audience might want something unusual.

Occasionally, this works. I'm unsure if it's a good idea. No stats, just my writing-time opinion. Writing every time is time-consuming and sometimes hazardous. Having a copy saved me duplication.

I can measure and learn from performance.

Copy of the product’s What and Why’s

Last, I identified communities that might demand the product. This became an exercise in creativity.

List of potential marketing channels

The MVP

So now it’s time to build.

A MVP can test my assumptions. Business may learn from it. Not low-quality. We should learn from the tiniest thing.

I like the example of how Dropbox did theirs. They assumed that if the product works, people will utilize it. How can this be tested without a quality product? They made a movie demonstrating the software's functionality. Who knows how much functionality existed?

So I tested my biggest assumption. Users want schema references. How can I test if users want to reference another schema? I'd love this. Recall taught me that wanting something doesn't mean others do.

I made an email-collection landing page. Describe it briefly. Reference library. Each email sender wants a reference. They're interested in the product. Few other reasons exist.

Header and footer were skipped. No name or logo. DbSchemaLibrary is a name I thought of after the fact. 5-minute logo. I expected a flop. Recall has no users after months of labor. What could happen to a 2-day project?

I didn't compromise learning validation. How many visitors sign up? To draw a conclusion, I must track these results.

Landing page

Posting Time

Now that the job is done, gauge interest. The next morning, I posted on all my channels. I didn't want to be spammy, therefore it required more time.

I made sure each channel had at least one fan of this product. I also answer people's inquiries in the channel.

My list stinks. Several channels wouldn't work. The product's target market isn't there. Posting there would waste our time. This taught me to create marketing channels depending on my persona.

Statistics! What actually happened

My favorite part! 23 channels received the link.

Results across the marketing channels

I stopped posting to Discord despite its high conversion rate. I eliminated some channels because they didn't fit. According to the numbers, some users like it. Most users think it's spam.

I was skeptical. And 12 people viewed it.

I didn't expect much attention on a startup subreddit. I'll likely examine Reddit further in the future. As I have enough info, I didn't post much. Time for the next validated learning

No comment. The post had few views, therefore the numbers are low.

The targeted people come next.

I'm a Toptal freelancer. There's a member-only Slack channel. Most people can't use this marketing channel, but you should! It's not as spectacular as discord's 27% conversion rate. But I think the users here are better.

I don’t really have a following anywhere so this isn’t something I can leverage.

The best yet. 10% is converted. With more data, I expect to attain a 10% conversion rate from other channels. Stable number.

This number required some work. Did you know that people use many different clients to read HN?

Unknowns

Untrackable views and signups abound. 1136 views and 135 signups are untraceable. It's 11%. I bet much of that came from Hackernews.

Overall Statistics

The 7-day signup-to-visit ratio was 17%. (Hourly data points)

Signup to Views percentageSignup to Views count

First-day percentages were lower, which is noteworthy. Initially, it was little above 10%. The HN post started getting views then.

Percentage of signups to views for the first 2 days

When traffic drops, the number reaches just around 20%. More individuals are interested in the connection. hn.algolia.com sent 2 visitors. This means people are searching and finding my post.

Percentage of signups after the initial traffic

Interesting discoveries

1. HN post struggled till the US woke up.

11am UTC. After an hour, it lost popularity. It seemed over. 7 signups converted 13%. Not amazing, but I would've thought ahead.

After 4pm UTC, traffic grew again. 4pm UTC is 9am PDT. US awakened. 10am PDT saw 512 views.

Signup to views count during the first few hours

2. The product was highlighted in a newsletter.

I found Revue references when gathering data. Newsletter platform. Someone posted the newsletter link. 37 views and 3 registrations.

3. HN numbers are extremely reliable

I don't have a time-lapse graph (yet). The statistics were constant all day.

  • 2717 views later 272 new users, or 10.1%

  • With 293 signups at 2856 views, 10.25%

  • At 306 signups at 2965 views, 10.32%

Learnings

1. My initial estimations were wildly inaccurate

I wrote 30% conversion. Reading some articles, looks like 10% is a good number to aim for.

2. Paying attention to what matters rather than vain metrics

The Lean Startup discourages vanity metrics. Feel-good metrics that don't measure growth or traction. Considering the proportion instead of the total visitors made me realize there was something here.

What’s next?

There are lots of work to do. Data aggregation, display, website development, marketing, legal issues. Fun! It's satisfying to solve an issue rather than investigate its cause.

In the meantime, I’ve already written the first project update in another post. Continue reading it if you’d like to know more about the project itself! Shifting from Quantity to Quality — DbSchemaLibrary

Dung Claire Tran

Dung Claire Tran

3 years ago

Is the future of brand marketing with virtual influencers?

Digital influences that mimic humans are rising.

Lil Miquela has 3M Instagram followers, 3.6M TikTok followers, and 30K Twitter followers. She's been on the covers of Prada, Dior, and Calvin Klein magazines. Miquela released Not Mine in 2017 and launched Hard Feelings at Lollapazoolas this year. This isn't surprising, given the rise of influencer marketing.

This may be unexpected. Miquela's fake. Brud, a Los Angeles startup, produced her in 2016.

Lil Miquela is one of many rising virtual influencers in the new era of social media marketing. She acts like a real person and performs the same tasks as sports stars and models.

The emergence of online influencers

Before 2018, computer-generated characters were rare. Since the virtual human industry boomed, they've appeared in marketing efforts worldwide.

In 2020, the WHO partnered up with Atlanta-based virtual influencer Knox Frost (@knoxfrost) to gather contributions for the COVID-19 Solidarity Response Fund.

Lu do Magalu (@magazineluiza) has been the virtual spokeswoman for Magalu since 2009, using social media to promote reviews, product recommendations, unboxing videos, and brand updates. Magalu's 10-year profit was $552M.

In 2020, PUMA partnered with Southeast Asia's first virtual model, Maya (@mayaaa.gram). She joined Singaporean actor Tosh Zhang in the PUMA campaign. Local virtual influencer Ava Lee-Graham (@avagram.ai) partnered with retail firm BHG to promote their in-house labels.

Maya and Tosh Zhang in PUMA Rider campaign. Credits to Vulcan Post

In Japan, Imma (@imma.gram) is the face of Nike, PUMA, Dior, Salvatore Ferragamo SpA, and Valentino. Imma's bubblegum pink bob and ultra-fine fashion landed her on the cover of Grazia magazine.

Imma on Grazia cover. Credits to aww.tokyo

Lotte Home Shopping created Lucy (@here.me.lucy) in September 2020. She made her TV debut as a Christmas show host in 2021. Since then, she has 100K Instagram followers and 13K TikTok followers.

Liu Yiexi gained 3 million fans in five days on Douyin, China's TikTok, in 2021. Her two-minute video went viral overnight. She's posted 6 videos and has 830 million Douyin followers.

Liu Yiexi’s video on Douyin. Credits to Ji Yuqiao on Global Times

China's virtual human industry was worth $487 million in 2020, up 70% year over year, and is expected to reach $875.9 million in 2021.

Investors worldwide are interested. Immas creator Aww Inc. raised $1 million from Coral Capital in September 2020, according to Bloomberg. Superplastic Inc., the Vermont-based startup behind influencers Janky and Guggimon, raised $16 million by 2020. Craft Ventures, SV Angels, and Scooter Braun invested. Crunchbase shows the company has raised $47 million.

The industries they represent, including Augmented and Virtual reality, were worth $14.84 billion in 2020 and are projected to reach $454.73 billion by 2030, a CAGR of 40.7%, according to PR Newswire.

Advantages for brands

Forbes suggests brands embrace computer-generated influencers. Examples:

  1. Unlimited creative opportunities: Because brands can personalize everything—from a person's look and activities to the style of their content—virtual influencers may be suited to a brand's needs and personalities.

  2. 100% brand control: Brand managers now have more influence over virtual influencers, so they no longer have to give up and rely on content creators to include brands into their storytelling and style. Virtual influencers can constantly produce social media content to promote a brand's identity and ideals because they are completely scandal-free.

  3. Long-term cost savings: Because virtual influencers are made of pixels, they may be reused endlessly and never lose their beauty. Additionally, they can move anywhere around the world and even into space to fit a brand notion. They are also always available. Additionally, the expense of creating their content will not rise in step with their expanding fan base.

  4. Introduction to the metaverse: Statista reports that 75% of American consumers between the ages of 18 and 25 follow at least one virtual influencer. As a result, marketers that support virtual celebrities may now interact with younger audiences that are more tech-savvy and accustomed to the digital world. Virtual influencers can be included into any digital space, including the metaverse, as they are entirely computer-generated 3D personas. Virtual influencers can provide brands with a smooth transition into this new digital universe to increase brand trust and develop emotional ties, in addition to the young generations' rapid adoption of the metaverse.

  5. Better engagement than in-person influencers: A Hype Auditor study found that online influencers have roughly three times the engagement of their conventional counterparts. Virtual influencers should be used to boost brand engagement even though the data might not accurately reflect the entire sector.

Concerns about influencers created by computers

Virtual influencers could encourage excessive beauty standards in South Korea, which has a $10.7 billion plastic surgery industry.

A classic Korean beauty has a small face, huge eyes, and pale, immaculate skin. Virtual influencers like Lucy have these traits. According to Lee Eun-hee, a professor at Inha University's Department of Consumer Science, this could make national beauty standards more unrealistic, increasing demand for plastic surgery or cosmetic items.

Lucy by Lotte Home Shopping. Credits to Lotte Home Shopping on CNN

Other parts of the world raise issues regarding selling items to consumers who don't recognize the models aren't human and the potential of cultural appropriation when generating influencers of other ethnicities, called digital blackface by some.

Meta, Facebook and Instagram's parent corporation, acknowledges this risk.

“Like any disruptive technology, synthetic media has the potential for both good and harm. Issues of representation, cultural appropriation and expressive liberty are already a growing concern,” the company stated in a blog post. “To help brands navigate the ethical quandaries of this emerging medium and avoid potential hazards, (Meta) is working with partners to develop an ethical framework to guide the use of (virtual influencers).”

Despite theoretical controversies, the industry will likely survive. Companies think virtual influencers are the next frontier in the digital world, which includes the metaverse, virtual reality, and digital currency.

In conclusion

Virtual influencers may garner millions of followers online and help marketers reach youthful audiences. According to a YouGov survey, the real impact of computer-generated influencers is yet unknown because people prefer genuine connections. Virtual characters can supplement brand marketing methods. When brands are metaverse-ready, the author predicts virtual influencer endorsement will continue to expand.

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Nick Babich

Nick Babich

2 years ago

Is ChatGPT Capable of Generating a Complete Mobile App?

Image generated using midjourney

TL;DR: It'll be harder than you think.

Mobile app development is a complicated product design sector. You require broad expertise to create a mobile app. You must write Swift or Java code and consider mobile interactions.

When ChatGPT was released, many were amazed by its capabilities and wondered if it could replace designers and developers. This article will use ChatGPT to answer a specific query.

Can ChatGPT build an entire iOS app?

This post will use ChatGPT to construct an iOS meditation app. Video of the article is available.

App concepts for meditation

After deciding on an app, think about the user experience. What should the app offer?

Let's ask ChatGPT for the answer.

Asking ChatGPT to describe a concept of a mediation app.

ChatGPT described a solid meditation app with various exercises. Use this list to plan product design. Our first product iteration will have few features. A simple, one-screen software will let users set the timeframe and play music during meditation.

Structure of information

Information architecture underpins product design. Our app's navigation mechanism should be founded on strong information architecture, so we need to identify our mobile's screens first.

ChatGPT can define our future app's information architecture since we already know it.

Asking ChatGPT, “what is a good structure for a mediation app for iOS?”

ChatGPT uses the more complicated product's structure. When adding features to future versions of our product, keep this information picture in mind.

Color palette

Meditation apps need colors. We want to employ relaxing colors in a meditation app because colors affect how we perceive items. ChatGPT can suggest product colors.

Asking ChatGPT to provide a color palette with hex colors that will contain brand color, as well as primary and secondary colors.

See the hues in person:

Listing colors provided by the ChatGPT

Neutral colors dominate the color scheme. Playing with color opacity makes this scheme useful.

Changing the opacity of the brand color in Figma.

Ambiance music

Meditation involves music. Well-chosen music calms the user.

Let ChatGPT make music for us.

Aksing ChatGPT to write music.

ChatGPT can only generate text. It directs us to Spotify or YouTube to look for such stuff and makes precise recommendations.

Fonts

Fonts can impress app users. Round fonts are easier on the eyes and make a meditation app look friendlier.

ChatGPT can suggest app typefaces. I compare two font pairs when making a product. I'll ask ChatGPT for two font pairs.

Ask ChatGPT to provide two font pairs for a meditation app.

See the hues in person:

Two font pairs generated by ChatGPT.

Despite ChatGPT's convincing font pairing arguments, the output is unattractive. The initial combo (Open Sans + Playfair Display) doesn't seem to work well for a mediation app.

Content

Meditation requires the script. Find the correct words and read them calmly and soothingly to help listeners relax and focus on each region of their body to enhance the exercise's effect.

ChatGPT's offerings:

Asking ChatGPT to write a meditation script.

ChatGPT outputs code. My prompt's word script may cause it.

Timer

After fonts, colors, and content, construct functional pieces. Timer is our first functional piece. The meditation will be timed.

Let ChatGPT write Swift timer code (since were building an iOS app, we need to do it using Swift language).

Aksing ChatGPT to write a code for a timer.

ChatGPT supplied a timer class, initializer, and usage guidelines.

Sample for timer initializer and recommendations on how to use it provided by ChatGPT.

Apple Xcode requires a playground to test this code. Xcode will report issues after we paste the code to the playground.

XCode shows error messages when use use a code generated by ChatGPT.

Fixing them is simple. Just change Timer to another class name (Xcode shows errors because it thinks that we access the properties of the class we’ve created rather than the system class Timer; it happens because both classes have the same name Timer). I titled our class Timero and implemented the project. After this quick patch, ChatGPT's code works.

Successful project build in Xcode using a modified version of a code provided by the ChatGPT.

Can ChatGPT produce a complete app?

Since ChatGPT can help us construct app components, we may question if it can write a full app in one go.

Question ChatGPT:

Asking ChatGPT to write a meditation app for iOS.

ChatGPT supplied basic code and instructions. It's unclear if ChatGPT purposely limits output or if my prompt wasn't good enough, but the tool cannot produce an entire app from a single prompt.

However, we can contact ChatGPT for thorough Swift app construction instructions.

Asking ChatGPT about instructions for building SwiftUI app.

We can ask ChatGPT for step-by-step instructions now that we know what to do. Request a basic app layout from ChatGPT.

Ask ChatGPT to generate a layout for the iOS app.

Copying this code to an Xcode project generates a functioning layout.

A layout built by XCode using the code provided by ChatGPT.

Takeaways

  • ChatGPT may provide step-by-step instructions on how to develop an app for a specific system, and individual steps can be utilized as prompts to ChatGPT. ChatGPT cannot generate the source code for the full program in one go.

  • The output that ChatGPT produces needs to be examined by a human. The majority of the time, you will need to polish or adjust ChatGPT's output, whether you develop a color scheme or a layout for the iOS app.

  • ChatGPT is unable to produce media material. Although ChatGPT cannot be used to produce images or sounds, it can assist you build prompts for programs like midjourney or Dalle-2 so that they can provide the appropriate images for you.

Bernard Bado

Bernard Bado

3 years ago

Build This Before Someone Else Does!

Captured by Mikhail Nilov

Do you want to build and launch your own software company? To do this, all you need is a product that solves a problem.

Coming up with profitable ideas is not that easy. But you’re in luck because you got me!

I’ll give you the idea for free. All you need to do is execute it properly.

If you’re ready, let’s jump right into it! Starting with the problem.

Problem

Youtube has many creators. Every day, they think of new ways to entertain or inform us.

They work hard to make videos. Many of their efforts go to waste. They limit their revenue and reach.

Solution

Content repurposing solves this problem.

One video can become several TikToks. Creating YouTube videos from a podcast episode.

Or, one video might become a blog entry.

By turning videos into blog entries, Youtubers may develop evergreen SEO content, attract a new audience, and reach a non-YouTube audience.

Many YouTube creators want this easy feature.

Let's build it!

Implementation

We identified the problem, and we have a solution. All that’s left to do is see how it can be done.

Monitoring new video uploads

First, watch when a friend uploads a new video. Everything should happen automatically without user input.

YouTube Webhooks make this easy. Our server listens for YouTube Webhook notifications.

After publishing a new video, we create a conversion job.

Creating a Blog Post from a Video

Next, turn a video into a blog article.

To convert, we must extract the video's audio (which can be achieved by using FFmpeg on the server).

Once we have the audio channel, we can use speech-to-text.

Services can accomplish this easily.

  • Speech-to-text on Google

  • Google Translate

  • Deepgram

Deepgram's affordability and integration make it my pick.

After conversion, the blog post needs formatting, error checking, and proofreading.

After this, a new blog post will appear in our web app's dashboard.

Completing a blog post

After conversion, users must examine and amend their blog posts.

Our application dashboard would handle all of this. It's a dashboard-style software where users can:

  • Link their Youtube account

  • Check out the converted videos in the future.

  • View the conversions that are ongoing.

  • Edit and format converted blog articles.

It's a web-based app.

Application diagram

It doesn't matter how it's made but I'd choose Next.js.

Next.js is a React front-end standard. Vercel serverless functions could conduct the conversions.

This would let me host the software for free and reduce server expenditures.

Taking It One Step Further

SaaS in a nutshell. Future improvements include integrating with WordPress or Ghost.

Our app users could then publish blog posts. Streamlining the procedure.

MVPs don't need this functionality.

Final Thoughts

Repurposing content helps you post more often, reach more people, and develop faster.

Many agencies charge a fortune for this service. Handmade means pricey.

Content creators will go crazy if you automate and cheaply solve this problem.

Just execute this idea!

Vitalik

Vitalik

4 years ago

An approximate introduction to how zk-SNARKs are possible (part 2)

If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.

Polynomials

Polynomials are a special class of algebraic expressions of the form:

  • x+5
  • x^4
  • x^3+3x^2+3x+1
  • 628x^{271}+318x^{270}+530x^{269}+…+69x+381

i.e. they are a sum of any (finite!) number of terms of the form cx^k

There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.

Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:

  • A(0)+B(0)=C(0)
  • A(1)+B(1)=C(1)
  • A(2)+B(2)=C(2)
  • A(3)+B(3)=C(3)

And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:

  • 12+1=13
  • 10+8=18
  • 15+8=23
  • 15+13=28

You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:

  • A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
  • B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
  • C(x)=5x+13

Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.

Comparing a polynomial to itself

You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)

As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.

Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).

Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!

Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.

see part 3