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Agent skill

Modular Arithmetic

by parcadei in parcadei/Continuous-Claude-v3

Problem-solving strategies for modular arithmetic in graph number theory

MITAuto-check: notesResearch & Science

Install Modular Arithmetic

skills CLI
$ npx skills add parcadei/Continuous-Claude-v3 --skill modular-arithmetic -a claude-code

Project install by default; add -g for ~/.claude/skills/.

GitHub CLI
$ gh skill install parcadei/Continuous-Claude-v3 modular-arithmetic --agent claude-code

Project scope by default; add --scope user for a personal install. Needs GitHub CLI 2.90.0 or later (public preview).

Manual copy
$ git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git skills-src && mkdir -p .claude/skills && cp -r skills-src/.claude/skills/math/graph-number-theory/modular-arithmetic .claude/skills/modular-arithmetic && rm -rf skills-src

Use ~/.claude/skills/ instead of .claude/skills for a personal install. The folder must contain SKILL.md.

Claude Code skills documentation · loads skills from .claude/skills/

Facts

Skill name
modular-arithmetic
GitHub stars
3.9k
Used in
1 other repo
Token cost
~505 tokens
SKILL.md length
187 words
Files
1
Skills in repo
141
Repo updated
First seen
Licence
MIT

At a glance

Problem-solving strategies for modular arithmetic in graph number theory

  • Works in 5 steps: Extended Euclidean Algorithm → Chinese Remainder Theorem → Euler's Theorem → …
  • Tasks that involve Math and symbolic computation
  • SKILL.md covers When to Use, Decision Tree, Tool Commands and Key Techniques, plus 1 more section
  • Calls uv

What it does

Modular Arithmetic is an agent skill from parcadei/Continuous-Claude-v3. Problem-solving strategies for modular arithmetic in graph number theory

Its SKILL.md is about 510 tokens, which your agent loads only when the skill is triggered. It is a single SKILL.md file with no bundled scripts.

It sits in Research & Science, covering Math and symbolic computation. It works with SymPy. The repository describes itself as: Context management for Claude Code. Hooks maintain state via ledgers and handoffs. MCP execution without context pollution. Agent orchestration with isolated context windows. The licence is MIT.

When your agent uses it

  • Tasks that involve Math and symbolic computation

Example prompts

  • “/modular-arithmetic”

Requirements

  • Python 3
  • Pre-approved tools (allowed-tools): Bash, Read

Workflow steps

5 steps, taken from the first numbered list in SKILL.md.

  1. Extended Euclidean Algorithm
  2. Chinese Remainder Theorem
  3. Euler's Theorem
  4. Quadratic Residues
  5. Order and Primitive Roots

What it can do on your machine

Read from SKILL.md and the folder at commit d07ff4b. It shows what the files ask for, not the result of running them.

  • Tool permissions

    Pre-approves these tools, so the agent can use them without asking each time:

    • Bash
    • Read

    From allowed-tools in the SKILL.md frontmatter.

  • Runs code

    Shell commands in SKILL.md call:

    • uv

    From the folder's file list and the shell code blocks in SKILL.md.

  • Network

    No URLs in SKILL.md. Its commands use uv, which can reach the network depending on how they are called.

    From URLs in SKILL.md, links to its own repository left out.

  • Credentials

    Names no API keys, tokens, secrets or passwords.

    From names ending in _API_KEY, _TOKEN, _SECRET, _KEY or _PASSWORD in SKILL.md.

Context cost

Modular Arithmetic loads about 505 tokens when it runs. Until then it costs about 23 tokens; SKILL.md has 187 words of instructions outside code blocks.

Always · name and description, kept in context so the agent knows when to use it
~23
When it runs · the whole SKILL.md, loaded when a task matches
~505

Estimates: characters ÷ 4, the usual rule of thumb; real counts depend on the model's tokenizer. Scripts and assets cost tokens only if the agent reads them.

Safety

Auto-check: notes

The automated check noted patterns worth knowing about, such as sudo or a known installer.

  • NotePre-approves every shell command (allowed-tools: Bash)SKILL.md
    allowed-tools: Bash, Read

Automated static check — not a guarantee. Review scripts before installing. It scans the text of SKILL.md for risky patterns (piping downloads into a shell, reading credential files, hidden Unicode, destructive commands); files beside SKILL.md are not scanned.

SKILL.md

The full file from parcadei/Continuous-Claude-v3 at commit d07ff4b, republished under its MIT licence (© parcadei). 187 words, ~505 tokens.

Download SKILL.mdSave it as .claude/skills/modular-arithmetic/SKILL.md (or your agent's skills folder).
name
modular-arithmetic
description
Problem-solving strategies for modular arithmetic in graph number theory
allowed-tools
Bash, Read

Modular Arithmetic

When to Use

Use this skill when working on modular-arithmetic problems in graph number theory.

Decision Tree

  1. Extended Euclidean Algorithm

    • Find gcd(a,b) and x,y with ax + by = gcd(a,b)
    • Modular inverse: a^{-1} mod n when gcd(a,n) = 1
    • sympy_compute.py solve "a*x == 1 mod n"

  2. Chinese Remainder Theorem

    • System x = a_i (mod m_i) with coprime m_i
    • Unique solution mod prod(m_i)
    • z3_solve.py prove "crt_solution_exists"

  3. Euler's Theorem

    • a^{phi(n)} = 1 (mod n) when gcd(a,n) = 1
    • phi(p^k) = p^{k-1}(p-1)
    • sympy_compute.py simplify "euler_phi"

  4. Quadratic Residues

    • Legendre symbol: (a/p) = a^{(p-1)/2} mod p
    • Quadratic reciprocity: (p/q)(q/p) = (-1)^{...}
    • Tonelli-Shanks for square roots

  5. Order and Primitive Roots

    • ord_n(a) = smallest k with a^k = 1 (mod n)
    • Primitive root: ord_n(a) = phi(n)

Tool Commands

Sympy_Mod_Inverse
bash
uv run python -m runtime.harness scripts/sympy_compute.py solve "a*x == 1 mod n" --var x
Z3_Crt
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "solution_exists_iff_pairwise_coprime"
Sympy_Euler_Phi
bash
uv run python -m runtime.harness scripts/sympy_compute.py simplify "phi(p**k) == p**(k-1)*(p-1)"
Z3_Quadratic_Residue
bash
uv run python -m runtime.harness scripts/z3_solve.py prove "legendre_symbol_multiplicative"

Key Techniques

From indexed textbooks:

  • [Graph Theory (Graduate Texts in Mathematics (173))] By N we denote the set of natural numbers, including zero. The set Z/nZ of integers modulo n is denoted by Zn; its elements are written as i := i + nZ. When we regard Z2 = {0, 1} as a eld, we also denote it as F2 = {0, 1}.

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.

© parcadei, MIT. Rendered from Markdown: HTML in the file is shown as text, images as links, and headings moved down two levels. Raw file

Files

Just SKILL.md in .claude/skills/math/graph-number-theory/modular-arithmetic of parcadei/Continuous-Claude-v3.

Open the folder on GitHubat commit d07ff4b

Used in 1 other repository

We found 1 copy of this SKILL.md (exact, near-identical or edited) in other folders, from 1 other GitHub owner. This page covers the copy in parcadei/Continuous-Claude-v3, which our catalogue first saw on October 7, 2026.

Compare with similar skills

Modular Arithmetic next to the 5 skills that share the most tags, products or categories with it. Stars are the repository's; “used in” counts other GitHub owners with a copy.

Modular Arithmetic compared with similar skills
SkillStarsUsed inTokensAuto-checkLicenceRepo updated
Modular Arithmetic this skillparcadei/Continuous-Claude-v33.9k1 repos~505Automated safety check: NotesMIT
SympyzLanqing/codex-claude-academic-skills4.6k16 repos~3.4kAutomated safety check: PassMIT
Edu Analytic Geometrywy51ai/edulab1.4k1 repos~1.6kAutomated safety check: PassApache-2.0
Edu Solid Geometrywy51ai/edulab1.4k1 repos~1.1kAutomated safety check: PassApache-2.0
Math Toolsananddtyagi/cc-marketplace6872 repos~1.3kAutomated safety check: PassNone
Edu Chem Reactionwy51ai/edulab1.4k—~1.2kAutomated safety check: PassApache-2.0

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Works with

Categories

Questions about Modular Arithmetic

What does Modular Arithmetic do?

Problem-solving strategies for modular arithmetic in graph number theory. Modular Arithmetic is an agent skill from parcadei/Continuous-Claude-v3.

When should I use Modular Arithmetic?

Modular Arithmetic fits situations like: tasks that involve Math and symbolic computation.

How do I install Modular Arithmetic in Claude Code?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill modular-arithmetic -a claude-code`. Or copy the skill folder (.claude/skills/math/graph-number-theory/modular-arithmetic in parcadei/Continuous-Claude-v3) into .claude/skills/modular-arithmetic in your project. Claude Code loads it when a task matches its description.

How do I install Modular Arithmetic in Codex?

Run `npx skills add parcadei/Continuous-Claude-v3 --skill modular-arithmetic -a codex`. Or copy the skill folder (.claude/skills/math/graph-number-theory/modular-arithmetic in parcadei/Continuous-Claude-v3) into .agents/skills/modular-arithmetic in your project. Codex loads it when a task matches its description.

Can I use Modular Arithmetic in Cursor, Gemini CLI or GitHub Copilot?

Cursor, Gemini CLI, GitHub Copilot and OpenCode also load SKILL.md folders. With the skills CLI, run `npx skills add parcadei/Continuous-Claude-v3 --skill modular-arithmetic -a cursor` (or -a gemini-cli, github-copilot or opencode for the others). To copy it by hand, put the folder in .cursor/skills/modular-arithmetic, .gemini/skills/modular-arithmetic, .github/skills/modular-arithmetic and .opencode/skills/modular-arithmetic in your project.

What does Modular Arithmetic need to run?

Going by SKILL.md and its folder, Modular Arithmetic needs the command-line tools its instructions call (uv). Our summary lists: Python 3. Its frontmatter pre-approves these tools: Bash, Read.

Does Modular Arithmetic access the network?

SKILL.md contains no URLs. Its commands use uv, which can reach the network depending on how they are called. This is read from the text; nothing was executed.

Is Modular Arithmetic safe to install?

Our automated static check of SKILL.md found notes only (pre-approves every shell command (allowed-tools: bash)), nothing it rates as a warning. It is not a guarantee. Review the folder before installing.

What licence does Modular Arithmetic use?

Modular Arithmetic is published under the MIT licence (the repository's licence). It allows redistribution, so the full SKILL.md is shown on this page.

How many tokens does Modular Arithmetic use?

About 505 tokens (SKILL.md is roughly 2k characters). Agents keep only the skill's name and description in context until a task matches; then they load SKILL.md in full.

What are the alternatives to Modular Arithmetic?

Skills that share tags, products or a category with Modular Arithmetic: Sympy (zLanqing/codex-claude-academic-skills, 4.6k stars), Edu Analytic Geometry (wy51ai/edulab, 1.4k stars), Edu Solid Geometry (wy51ai/edulab, 1.4k stars) and Math Tools (ananddtyagi/cc-marketplace, 687 stars). The comparison table on this page puts their stars, adoption, token cost, safety result and licence side by side.

Who maintains Modular Arithmetic?

parcadei (a GitHub user) maintains it in parcadei/Continuous-Claude-v3, which has 3,940 GitHub stars. The repository holds 141 skills in this directory. The repository was last updated on January 26, 2026.

Source: parcadei/Continuous-Claude-v3 on GitHub. Facts on this page come from the repository at the commit we read; the author's words are quoted as theirs.