Add music
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title = "setup"
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title = "Setup"
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# setup
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# Setup
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List of software and services I use and endorse, mostly FOSS.
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List of software and services I use and endorse, mostly FOSS.
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## desktop
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## Desktop
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- [**Arch Linux**](https://archlinux.org/) OS with rolling releases.
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- [**Arch Linux**](https://archlinux.org/) OS with rolling releases.
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- [**Home manager**](https://github.com/nix-community/home-manager) Dotfile manager.
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- [**Home manager** (MIT)](https://github.com/nix-community/home-manager) Dotfile manager.
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- [**Firefox**](https://www.mozilla.org/firefox) Browser.
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- [**Firefox** (MPL-2.0)](https://www.mozilla.org/firefox) Browser.
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- [**Evolution**](https://wiki.gnome.org/Apps/Evolution) Email + calendar client.
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- [**Thunderbird** (MPL-2.0)](https://www.thunderbird.net) Email + calendar client.
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## development
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## Development
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- [**Neovim**](https://neovim.io/) Text editor.
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- [**Neovim** (Apache-2.0/Vim)](https://neovim.io/) Text editor.
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## server
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## Server
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- [**NixOS**](https://nixos.org/) Declarative and reproducible operating system.
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- [**NixOS** (MIT)](https://nixos.org/) Declarative and reproducible operating system.
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- [**Hugo**](https://gohugo.io/) Static site generator that powers this site.
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- [**Hugo** (Apache-2.0)](https://gohugo.io/) Static site generator that powers this site.
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- [**Gitea**](https://gitea.io) Self-hosted git.
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- [**Gitea** (MIT)](https://gitea.io/) Self-hosted git.
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## mobile
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## Mobile
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- [**DAVx5**](https://www.davx5.com/) CalDAV and CardDAV sync for Android.
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- [**DAVx5** (GPL-3.0)](https://www.davx5.com/) CalDAV and CardDAV sync for Android.
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- [**Shuttle**](https://www.shuttlemusicplayer.com/) Music player.
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- [**Gadgetbridge** (AGPL-3.0)](https://gadgetbridge.org/) Smartwatch client.
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- [**Gadgetbridge**](https://gadgetbridge.org/) Smartwatch client.
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- [**K-9 Mail** (Apache-2.0)](https://k9mail.app/) Mail client.
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- [**K-9 Mail**](https://k9mail.app/) Mail client.
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- [**Feeder** (GPL-3.0)](https://f-droid.org/packages/com.nononsenseapps.feeder/) RSS aggregator.
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- [**Feeder**](https://f-droid.org/packages/com.nononsenseapps.feeder/) RSS aggregator.
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## services
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## Music
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- [**ProtonMail**](https://protonmail.com/) Encrypted email.
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- [**Navidrome** (GPL-3.0)](https://navidrome.com) Self-hosted Subsonic-compatible streaming server.
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- [**Signal**](https://signal.org/) Encrypted chat.
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- [**Sublime Music** (GPL-3.0)](https://sublimemusic.app) GTK Subsonic-compatible music client.
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- [**Subtracks** (GPL-3.0)](https://github.com/austinried/subtracks) Android Subsonic-compatible music client.
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## Services
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- [**SourceHut** (AGPL-3.0)](https://sourcehut.org) Git, mailing list, IRC bouncer, etc. hosting.
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- [**Element**](https://element.io/) Federated chat provider.
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- [**Element**](https://element.io/) Federated chat provider.
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- [**ProtonMail** (Proprietary)](https://protonmail.com/) Encrypted email.
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- [**Signal** (GPL-3.0/AGPL-3.0)](https://signal.org/) Encrypted chat.
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## games
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## Games
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Mostly from Steam.
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Mostly from Steam.
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@ -32,22 +32,30 @@ first, but there are some important differences to note:
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- We're not given the public keys $e_1$ and $e_2$, but they are related through
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- We're not given the public keys $e_1$ and $e_2$, but they are related through
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$x$.
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$x$.
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[Rabin]: https://en.wikipedia.org/wiki/Rabin_cryptosystem
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## Finding $e_1$ and $e_2$
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## Finding $e_1$ and $e_2$
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We know that $e_1$ and $e_2$ are related through $x$, which is some even number
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We know that $e_1$ and $e_2$ are related through $x$, which is some even number
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greater than 2, but we're not given any of their real values. We're also given
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greater than 2, but we're not given any of their real values. We're also given
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through an oddly-named `functor` function that:
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through an oddly-named `functor` function that:
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$$
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$$ 1 + e_1 + e_1^2 + \cdots + e_1^x = 1 + e_2 + e_2^2 $$
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\begin{aligned}
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1 + e_1 + e_1^2 + \cdots + e_1^x &= 1 + e_2 + e_2^2 \\\
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\frac{1 - e_1^x}{1 - e_1} &= 1 + e_2 + e_2^2
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\end{aligned}
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$$
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Interestingly enough, since $e_1$ and $e_2$ are primes, that means
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Taking the entire equation $\mod e_1$ gives us:
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$$\begin{aligned}
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1 &\equiv 1 + e_2 + e_2^2 \mod e_1 \\\
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0 &\equiv e_2 + e_2^2 \\\
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0 &\equiv e_2(1 + e_2)
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\end{aligned}$$
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This means there are two possibilities: either $e_1 = e_2$ or $e_1$ is even
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(since we know $e_2$ is a prime). The first case isn't possible, because with $x
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\> 2$, the geometric series equation would not be satisfied. So it must be true
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that $\boxed{e_1 = 2}$, the only even prime.
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Applying geometric series expansion, $1 + e_2 + e_2^2 = 2^x - 1$.
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I'd like to thank @10, @sahuang, and @thebishop in the Project Sekai discord for
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I'd like to thank @10, @sahuang, and @thebishop in the Project Sekai discord for
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their help throughout this challenge.
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doing a lot of the heavy-lifting to solve this challenge.
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[Rabin]: https://en.wikipedia.org/wiki/Rabin_cryptosystem
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