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I'm currently dealing with a computer science problem and got stuck trying to proof different assumptions I made. One of these assumptions is that if $a$ and $b$ are some arbitrary numbers and $t$ is their biggest common divisor then you can write any number $x=l t$ with $l\in\mathbb{Z}$ as $x=na-mb$ with some (non negativ) integers $n$ and $m$. Thus, when $a$ and $b$ are prime numbers then you are abel to write any number $x\in\mathbb{Z}$ that way. Since I still go to high school I may not know some tools for solving this but maybe someone has an idea on how to proofe this.

Thanks for your help, and please excuse some language mistakes I may have made - english is not my first languag.

Bill Dubuque
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Silvaner
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Bézout's identity is that exact theorem:

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

Silvaner
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