Modular arithmetic with exact integers

Add, subtract, multiply, exponentiate or find a modular inverse. Inspect Euclidean division steps and export exact integer strings without floating-point rounding.

Use whole numbers such as -17, 0 or 25, with at most 256 digits. The modulus m must be at least 2; for exponentiation, b must be at least 0. Results are remainders from 0 to m - 1.

Operation

Integer aInteger b (exponent for powers)

Modulus m

The modular inverse exists only when a and m have no common divisor greater than 1. The displayed steps calculate their greatest common divisor (GCD). This educational tool does not guarantee constant execution time and is not designed for cryptographic protection.

Quick start

Add, subtract, multiply, exponentiate or find a modular inverse. Inspect Euclidean division steps and export exact integer strings without floating-point rounding.

Enter your own data and check units and assumptions.
Calculate using the action button and review the result below.
Export the last successful report; recalculate after editing inputs.

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Modular arithmetic with exact integers