## 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.

If you enter very large numbers—having 17 digits, for example—the calculator may return incorrect results. This is due to the inherent limitations of the way computers do arithmetic, using floating-point numbers. If you need to work very large numbers, try the Big Integer Modular Arithmetic Calculator (Big MAC), which uses the Perl bigint module to handle large integers.

**Notes:**

- 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).

- - a returns m - a, the additive inverse of a.

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

Copyright 2009 by Paul Trow