Can someone help me understand this statement:
If $ax+by=d$ then $\gcd(a,b)$ divides $d$.
Bezout's identity states that:
the greatest common divisor $d$ is the smallest positive integer that can be written as $ax + by$
However the definition of $\gcd(a, b)$ is the largest positive integer which divides both $a$ and $b$.
I'm am completely lost.
If anyone could provide some sort of layout to help me sort this out I would be really happy.
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