Modular Arithmetic Calculator Field Guide: When Five Operations, One Bezout Identity, and the Bit-Length Rule Decide Whether Your Modular Computation Is Exact or a Free Estimate

Modular arithmetic field guide: five operations (add, subtract, multiply, inverse, power) with BigInt precision up to 10^18. Walks through the extended Euclidean algorithm for inverse, square-and-multiply for power, and the canonical [0, m-1] representative.