Solve Modular Arithmetic
技能 已验证 活跃Solve modular arithmetic problems including congruences, systems via the Chinese Remainder Theorem, modular inverses, and Euler's theorem applications. Covers both manual and computational approaches. Use when solving linear congruences, computing modular inverses, evaluating large modular exponentiations, working with simultaneous congruences (CRT), or operating in cyclic groups and discrete logarithm contexts.
To provide a structured and reliable method for solving complex modular arithmetic problems, aiding users in mathematical computations and theoretical explorations.
功能
- Solves single linear congruences
- Applies Chinese Remainder Theorem for systems
- Computes modular inverses using Extended Euclidean Algorithm
- Evaluates modular exponentiations via Euler's theorem and repeated squaring
- Verifies all solutions by substitution
使用场景
- Solving linear congruences ax = b (mod m)
- Working with simultaneous congruences (CRT)
- Computing modular inverses
- Evaluating large modular exponentiations
- Exploring cyclic groups and discrete logarithms
非目标
- Solving arbitrary algebraic equations
- Performing symbolic calculus
- General number theory exploration beyond modular arithmetic
工作流
- Parse the Congruence System or Modular Equation
- Solve a Single Congruence (if applicable)
- Solve a System via the Chinese Remainder Theorem (if applicable)
- Apply Euler's Theorem or Fermat's Little Theorem (if applicable)
- Verify Solution by Substitution
安装
/plugin install agent-almanac@pjt222-agent-almanac质量评分
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