Saturday, 10 March 2018

elementary number theory - Why is it true that if $ax+by=d$ then $gcd(a,b)$ divides $d$?

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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