# Bézout coefficients

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

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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'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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