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"