# Bézout coefficients

This online calculator computes Bézout's coefficients for two given integers, and represents them in the general form

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

**Bézout's identity** and **Bézout's coefficients**

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

Let

aandbbe integers with the greatest common divisord. Then, there exist integersxandysuch thatax+by=d. More generally, the integers of the formax+byare exactly the multiples ofd.

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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