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# Bézout coefficients

This online calculator computes Bézout's coefficients for two given integers and represented them in the general form This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/8586/. Also, please do not modify any references to the original work (if any) contained in this content.

You can use this calculator to obtain pair of Bézout's coefficients and the general form of Bézout's coefficients as well. Some theory can be found below the calculator #### Bézout coefficients

First coefficient

Second coefficient

General form

Bézout's identity and Bézout's coefficients

To recap, the Bézout's identity (aka Bézout's lemma) is the following statement:

Let a and b be integers with greatest common divisor d. Then, there exist integers x and y such that ax + by = d. More generally, the integers of the form ax + by are exactly the multiples of d.

If d is the greatest common divisor of integers a and b, and x, y is any pair of Bézout's coefficients, the general form of Bézout's coefficients is

and the general form of Bézout's identity is

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