## Modular Arithmetic Calculator

Welcome to the Modular Arithmetic Calculator, which performs arithmetic modulo an integer m (called the *modulus*).

To use the calculator, enter a non-zero integer for the modulus m, and integers a and b below. Then press one of the operation buttons.

**Notes:**

- If you enter very large numbers—having, say, 17 digits—the calculator might return incorrect results. This is due to the inherent limitations of computer arithmetic on floating-point numbers. If you need to do calculations with very large numbers, try the Big Integer Modular Arithmetic Calculator (Big MAC), which uses the Perl bigint module.

- 1 / a (the multiplicative inverse of a) exists if and only if the greatest common divisor of a and m is 1. See Greatest Common Divisor.

- Square roots are only calculated when the modulus m is a prime number (using the Tonelli-Shanks algorithm). If r is a square root of a, so is m - r. For example, since 3 is a square root of 9 modulo 17, the other square root of 9 is 14 (= 17 - 3).

Please send any comments or suggestions for improving the Modular Arithmetic Calculator. Paul Trow's math page.

Copyright 2009 by Paul Trow