## Modular Arithmetic Calculator

Welcome to the Modular Arithmetic Calculator, which performs arithmetic modulo an integer m (called the *modulus*). Modular arithmetic has many important applications. For example, whenever you make a purchase over the internet, or a call on your cell phone, the data that is transimitted is encoded using methods based on modular arithmatic.

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. The answer is displayed next to **Result**.

**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). After calculating a square root, click
**+/- Result** to get the other root.

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

Copyright 2009 by Paul Trow