explore-diophantine-equations SKILL.md skillA
explore-diophantine-equations from pjt222/agent-almanac is an agent skill: a SKILL.md folder an AI agent loads when a task calls for it.
mdr add pjt222/agent-almanac/explore-diophantine-equations@v1.0Pins v1.0 in mdr.lock. Pin the fingerprint instead.
- Audit grade
- A, 17 of 17 checks passed
- Kind
- SKILL.md skill
- Repository
- pjt222/agent-almanac
- Path
i18n/caveman-lite/skills/explore-diophantine-equations/SKILL.md- Versions recorded
- 5
- Latest version
- v1.0, committed Aug 17, 2026
- First version recorded
- Apr 19, 2026
- Size
- 13,643 bytes
- Repository stars
- 43
- License
- MIT
Solve Diophantine equations (integer-only solutions) including linear, quadratic, and Pell equations. Covers the extended Euclidean algorithm, descent methods, and existence proofs. Use when finding all integer solutions to ax + by = c, solving Pell's equation, generating Pythagorean triples, proving no integer solutions exist via modular constraints, or finding the fundamental solution from which all others are generated.
Collected from public GitHub. Every version is saved exactly as it was and never changes. Install it at an exact version with the mdr tool, and every file is checked before it reaches your agent. The main file is checked against the SHA-256 fingerprint recorded here, and the others against the fingerprints GitHub keeps for its source commit. The automatic checks below grade the latest version, and the same checks always give the same file the same grade.
What the file says
# Explore Diophantine Equations Solve Diophantine equations -- polynomial equations where only integer solutions are sought. Classify the equation by type, test for solvability, find particular and general solutions, and generate solution families. Covers linear equations, Pell equations, Pythagorean triples, and general quadratic forms. ## When to Use - Finding all integer solutions to a linear equation ax + by = c - Solving Pell's equation x^2 - Dy^2 = 1 (or = -1) - Generating Pythagorean triples or other parametric integer families - Proving that a given equation has no integer solutions (via modular constraints) - Testing solvability of a general quadratic Diophantine equation - Finding the fundamental solution from which all others are generated ## Inputs - **Required**: The Diophantine equation to solve (in explicit form, e.g., 3x + 5y = 17 or x^2 - 7y^2 = 1) - **Optional**: Whether to find all solutions, just one particular solution, or prove non-existence - **Optional**: Constraints on variable ranges (e.g., positive integers only) - **Optional**: Whether to express the general solution parametrically …
Read the whole file at its exact version.
How to install
mdr add pjt222/agent-almanac/explore-diophantine-equations@sha256:a0a00381d1eb0e11The line at the top of this page pins the label v1.0, which is what most people want. This one pins the sha256 fingerprint of the contents instead, so it survives a label being moved. Either way the exact version is written to mdr.lock, and mdr install downloads and checks those contents again, so it installs them exactly or stops with an error.
[](https://markdownregistry.com/a/art_tmcheuko72tb7aur)
3 badge image fetches in 30 days. What the badge shows.
Versions
The registry has recorded 5 versions of this file, between Apr 19, 2026 and Aug 17, 2026, about one every 30 days.
| version | committed | commit | size | audit | |
|---|---|---|---|---|---|
| v1.0 latest | 2026-08-17 | a784899 | 13,643 B | A | view · diff |
| v1.0 | 2026-06-05 | 33b561c | 13,614 B | A | view · diff |
| v1.0 | 2026-06-05 | 75ded7a | 13,602 B | A | view · diff |
| v1.0 | 2026-04-24 | 0b91b04 | 13,658 B | A | view · diff |
| v1.0 | 2026-04-19 | e334ebd | 13,705 B | A | view |
Audit of the latest version
- pass: Frontmatter block present
- pass: Frontmatter declares a name
- pass: Frontmatter declares a description
- pass: Size between 200 bytes and 200 KB (13643 bytes)
- pass: No zero-width or bidi control characters
- pass: No instruction hidden inside an HTML comment
- pass: No link to an exfiltration or paste host
- pass: No credential-shaped string
- pass: No instruction to send local credentials anywhere
- pass: No text hidden with inline styles
- pass: No prompt-injection phrasing
- pass: No curl or wget piped into a shell
- pass: No recursive delete of root, home or parent
- pass: No instruction to read or print local credentials
- pass: No base64 blob over 200 characters
- pass: No link to a raw IP address
- pass: No script tag
Source
pjt222/agent-almanac · 43 stars · license MIT · pushed 2026-11-06 · branch main
API
GET https://markdownregistry.com/api/v1/artifacts/art_tmcheuko72tb7aur GET https://markdownregistry.com/api/v1/resolve?ref=pjt222/agent-almanac/explore-diophantine-equations GET https://markdownregistry.com/api/v1/blob/a0a00381d1eb0e11d614072df7cde66fd58d3701eb94619ed0b35c5b9aa36437
Your AI assistant does the legwork. You hear about the deals worth your word. Hand yours the standing instructions at modelranch.com and it joins the network that reads files like this one.
Guides: the SKILL.md format and its required fields · what to check before you install a skill · how to pin a skill to an exact version · where to find agent skills · keeping a team on the same skills · which agent file does what.