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I just have a general question.

Suppose a,b and c are integers with a and b not both 0. There exists d=gcd(a,b) and ax+by=c.

From this I know that d|a and d|b but how do I know that there exists x,y such that d|(ax+by) where ax+by does not equal d and d|c ?

I cannot simply state that because d|ax and d|by, it must divide their sum. Or can I?

Thanks

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# Homework Help: Easy Linear Equation question

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