Modular Arithmetic Calculator

Welcome to the Modular Arithmetic Calculator, which performs arithmetic modulo an integer (also known as "clock arithmetic"). Modular arithmetic is essential to many aspects of communication in today's world, including:

Public key cryptography, which keeps your personal information secure when you make financial transactions over the Web.
Error-correcting codes, which make it possible to enjoy clear cell phone calls despite interference in the call channel.

To use the Modular Arithmetic 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 in the Result box.

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.

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Paul Trow's math software.

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