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When do the multiples of two primes span all large enough natural numbers?

If $m,n$ are positive integers and $(m,n)=1$.

What's the largest integer $N$ that cannot be expressed as $N=am+bn$, where $a$ and $b$ are nonnegative integers?

The answer is $N=mn-m-n$. How to prove it?

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    This is basically a duplicate of http://math.stackexchange.com/questions/8186/when-do-the-multiples-of-two-primes-span-all-large-enough-natural-numbers2011-01-30
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    Another question asked what $N$ is, but Qiaochu Yuan's answer there gives a proof as well: http://math.stackexchange.com/questions/8186/when-do-the-multiples-of-two-primes-span-all-large-enough-natural-numbers/8187#81872011-01-30
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    This is the $n=2$ case of the Frobenius problem. http://en.wikipedia.org/wiki/Frobenius_problem" (also known as the "coin problem"). The result you quote is due to Sylvester.2011-01-30
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    so shall we close it.2011-01-30

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