Solve Modular Arithmetic

Funktionen

• 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

Anwendungsfälle

• 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

Nicht-Ziele

• Solving arbitrary algebraic equations
• Performing symbolic calculus
• General number theory exploration beyond modular arithmetic

Workflow

1. Parse the Congruence System or Modular Equation
2. Solve a Single Congruence (if applicable)
3. Solve a System via the Chinese Remainder Theorem (if applicable)
4. Apply Euler's Theorem or Fermat's Little Theorem (if applicable)
5. Verify Solution by Substitution