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Let $a,b$ be positive relatively prime integers and $S$ be a set defined by $\{ax+by: x,y\in \mathbb{Z^+} \}$. I want to show that $ab-a-b$ is the maximum element in $\mathbb{N} \setminus S$.

We need to show that $ab-a-b+k \in S$ for all positive integers $k$ and $ab-a-b$ is not in $S$. Do you have any idea? Thanks.

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marked as duplicate by Bill Dubuque elementary-number-theory Mar 22 at 19:29

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