Question: Is the following statement true?
Statement: Let $a, b \ge 1$ be coprime numbers. Then $\exists N \ge 0 $ $\forall n \ge N$ $\exists u, v \ge 0$ with $n=au+bv$.
Let $N(a,b)$ be the smallest possible $N$. Then $N(a,b) = (a-1)(b-1)$.
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Sebastien Palcoux
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3Yes. If memory serves, $N-1$ is called the Frobenius number of $a$ and $b$. – Daniel Fischer Jul 08 '17 at 12:23
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1See https://en.wikipedia.org/wiki/Coin_problem. – lhf Jul 08 '17 at 13:30