{"id":22295859,"url":"https://github.com/meithecatte/isabelle-math-contests","last_synced_at":"2026-01-05T23:04:21.600Z","repository":{"id":98788392,"uuid":"301376572","full_name":"meithecatte/isabelle-math-contests","owner":"meithecatte","description":"Solutions to math olympiad problems in Isabelle/HOL","archived":false,"fork":false,"pushed_at":"2021-05-29T22:20:13.000Z","size":7272,"stargazers_count":11,"open_issues_count":0,"forks_count":0,"subscribers_count":2,"default_branch":"built-pdfs","last_synced_at":"2025-01-30T19:49:15.773Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":null,"has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/meithecatte.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2020-10-05T10:53:07.000Z","updated_at":"2024-12-07T10:59:41.000Z","dependencies_parsed_at":"2023-05-25T09:15:17.074Z","dependency_job_id":null,"html_url":"https://github.com/meithecatte/isabelle-math-contests","commit_stats":null,"previous_names":[],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/meithecatte%2Fisabelle-math-contests","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/meithecatte%2Fisabelle-math-contests/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/meithecatte%2Fisabelle-math-contests/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/meithecatte%2Fisabelle-math-contests/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/meithecatte","download_url":"https://codeload.github.com/meithecatte/isabelle-math-contests/tar.gz/refs/heads/built-pdfs","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245556344,"owners_count":20634881,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2024-12-03T17:43:22.118Z","updated_at":"2026-01-05T23:04:16.539Z","avatar_url":"https://github.com/meithecatte.png","language":null,"funding_links":[],"categories":[],"sub_categories":[],"readme":"# Isabelle/HOL solutions to math contest problems\n\nThis repository contains various [Isabelle/HOL] formal proofs. This is mostly solutions\nto interesting math olympiad problems, but some higher math exercises have found their way\nhere, too.\n\nApart from that, I keep some [notes] on the mathematical library of Isabelle. This includes\nsituations where the structure and interaction of objects \n\nI encourage you to explore.\n\n[notes]: https://github.com/NieDzejkob/isabelle-math-contests/blob/master/NOTES.md\n[Isabelle/HOL]: https://isabelle.in.tum.de/\n\n## Problems by tag\n\n- \u003cdetails\u003e\n  \u003csummary\u003enumber theory [\u003ci\u003e8 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [BMO1 2015 Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/BMO1/2015/BMO1-2015-Problem_2.pdf) (number theory)\n  - [Canada MO 2020 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Canada_MO/2020/Canada_MO-2020-Problem_1.pdf) (number theory)\n  - [Greece MO 2007 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Greece_MO/2007/Greece_MO-2007-Problem_1.pdf) (number theory)\n  - [Polish MO 1969 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)\n  - [Polish MO 1969 Round 1 Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)\n  - [Polish MO 2020 Round 1 Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_3.pdf) (number theory)\n  - [Polish MO 2020 Round 2 Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_3.pdf) (number theory)\n  - [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003ecombinatorics [\u003ci\u003e4 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [APMO 2013 Problem 4](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/APMO/2013/APMO-2013-Problem_4.pdf) (combinatorics)\n  - [IMO 2019 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_5.pdf) (combinatorics)\n  - [Polish MO 2020 Round 2 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_1.pdf) (combinatorics)\n  - [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003efunctional equation [\u003ci\u003e3 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Deltami 44M Problem 789](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Deltami_44M/Deltami_44M-Problem_789.pdf) (functional equation)\n  - [IMO 2019 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_1.pdf) (functional equation)\n  - [Unknown Origin Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Unknown_Origin/Unknown_Origin-Problem_1.pdf) (functional equation)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003ereal analysis [\u003ci\u003e3 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [IMC PoTD 15](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMC/IMC-PoTD_15.pdf) (real analysis)\n  - [Polish MO 1969 Round 1 Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_2.pdf) (real analysis)\n  - [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003einequality [\u003ci\u003e3 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_5.pdf) (inequality)\n  - [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)\n  - [Polish MO 2020 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_1.pdf) (inequality)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003egroup theory [\u003ci\u003e2 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Napkin Problem 1A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1A.pdf) (group theory)\n  - [Napkin Problem 1B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1B.pdf) (group theory)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003ediophantine equation [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003econgruences [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003emultiple solutions [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eequation over reals [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Warmup Problem C](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_C.pdf) (equation over reals)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003emetric space [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003egeometry [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Polish MO 1969 Round 1 Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)\n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003enondeterministic process [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [USAMO 2006 Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)\n  \u003c/details\u003e\n\n## Problems by origin\n\n- \u003cdetails\u003e\n  \u003csummary\u003eAsia Pacific Math Olympiad [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2013\n    - [Problem 4](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/APMO/2013/APMO-2013-Problem_4.pdf) (combinatorics)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eBritish Maths Olympiad Round 1 [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2015\n    - [Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/BMO1/2015/BMO1-2015-Problem_2.pdf) (number theory)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eCanada Math Olympiad [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2020\n    - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Canada_MO/2020/Canada_MO-2020-Problem_1.pdf) (number theory)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eDeltami 44M [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Problem 789](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Deltami_44M/Deltami_44M-Problem_789.pdf) (functional equation)\n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eGreece Math Olympiad [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2007\n    - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Greece_MO/2007/Greece_MO-2007-Problem_1.pdf) (number theory)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eInstagram Math Community [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [PoTD 15](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMC/IMC-PoTD_15.pdf) (real analysis)\n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eInternational Math Olympiad [\u003ci\u003e2 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2019\n    - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_1.pdf) (functional equation)\n    - [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/IMO/2019/IMO-2019-Problem_5.pdf) (combinatorics)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eAn Infinitely Large Napkin [\u003ci\u003e2 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Problem 1A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1A.pdf) (group theory)\n  - [Problem 1B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Napkin/Napkin-Problem_1B.pdf) (group theory)\n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003ePolish Math Olympiad [\u003ci\u003e11 problems\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 1969\n    - Round 1\n      - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_1.pdf) (number theory, diophantine equation)\n      - [Problem 2](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_2.pdf) (real analysis)\n      - [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Problem_5.pdf) (inequality)\n      - [Warmup Problem A](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_A.pdf) (number theory, congruences)\n      - [Warmup Problem B](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_B.pdf) (inequality, multiple solutions, real analysis)\n      - [Warmup Problem C](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_C.pdf) (equation over reals)\n      - [Warmup Problem D](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/1969/Round_1/Polish_MO-1969-Round_1-Warmup_Problem_D.pdf) (metric space, geometry)\n      \n    \n  - 2020\n    - Round 1\n      - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_1.pdf) (inequality)\n      - [Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_1/Polish_MO-2020-Round_1-Problem_3.pdf) (number theory)\n      \n    - Round 2\n      - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_1.pdf) (combinatorics)\n      - [Problem 3](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Polish_MO/2020/Round_2/Polish_MO-2020-Round_2-Problem_3.pdf) (number theory)\n      \n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eUnited States of America Math Olympiad [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - 2006\n    - [Problem 5](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/USAMO/2006/USAMO-2006-Problem_5.pdf) (number theory, combinatorics, nondeterministic process)\n    \n  \n  \u003c/details\u003e\n- \u003cdetails\u003e\n  \u003csummary\u003eUnknown Origin [\u003ci\u003e1 problem\u003c/i\u003e]\u003c/summary\u003e\n  \n  - [Problem 1](https://github.com/NieDzejkob/isabelle-math-contests/blob/built-pdfs/Unknown_Origin/Unknown_Origin-Problem_1.pdf) (functional equation)\n  \n  \u003c/details\u003e\n\n\n## Structure of this repository\n\nRaw Isabelle `.thy` files are hard to look at. As can be expected for math,\nlots of non-ASCII characters are involved. Apart from font issues, Isabelle actually\npredates Unicode, so the text files are actually encoded with LaTeX-ish escape sequences.\n\nThis motivates a sophisticated CI setup (the three words you don't ever want to see next\nto each other). The `master` branch of the repository keeps the sources, while GitHub\nActions render PDFs and push them onto the `built-pdfs` branch.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmeithecatte%2Fisabelle-math-contests","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmeithecatte%2Fisabelle-math-contests","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmeithecatte%2Fisabelle-math-contests/lists"}