# Documentation

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# `numlib`::`igcdmult`

Extended Euclidean algorithm for integers

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## Syntax

```numlib::igcdmult(`par1`, `par2, …`)
```

## Description

`numlib::igcdmult` is an extension of the kernel function `igcdex`.

`numlib::igcdmult` returns an error if the arguments evaluate to numbers which are not all of the correct type.

For integers `a_1,a_2,...,a_n`, `numlib::igcdmult(a_1,a_2,...,a_n)` returns a list [d, v1, …, vn] of integers such that `d` is the nonnegative greatest common divisor of `a_1,a_2,...,a_n` and ```d = a_1*v_1 + a_2*v_2 + ...+ a_n*v_n```.

For integers `a_1,a_2,...,a_n`, `numlib::igcdmult(a_1,a_2,...,a_n)` returns a list [d, v1, …, vn] of integers such that `d` is the nonnegative greatest common divisor of `a_1,a_2,...,a_n` and ```d = a_1*v_1 + a_2*v_2 + ...+ a_n*v_n```.

## Examples

### Example 1

Computing the greatest non-negative common divisor d of 455, 385, 165, 273 and integers v1, v2, v3, v4 such that d = 455 v1 + 385 v2 + 165 v3 + 273 v4:

`numlib::igcdmult(455,385,165,273)`

## Parameters

 `par1` Integer `par2, …` Integers

## Return Values

List of integers, or the function call with evaluated arguments if some argument is not a number.