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It is given that $a$ and $b$ are coprime positive integers. My question is, what is the largest integer $k$ such that the diophantine equation $ax+by=k$ does not have any solution where $x$ and $y$ are nonnegative integers ?

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This $k$ is called the Frobenius number and equals $ab-a-b$ (http://en.wikipedia.org/wiki/Frobenius_number#n_.3D_2).

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