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arXiv · 2108.02004

The maximum of the complementary of a semigroup with restricted conditions

Antonio Linero-Bas·Daniel Nieves-Roldán
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Abstract

We consider the set $$\mathcal{A} = \left\{10\cdot a + 11\cdot b \ | \gcd(a,b)=1, a\geq 1, b\geq 2a+1 \right\}.$$ We will prove that $\mathcal{A}$ is unbounded and that there exists a natural number $M\notin \mathcal{A}$ for which $$\left\{M+m:m\geq 1,m\in\mathbb N\right\}\subset \mathcal{A}.$$ Indeed, such number is $M = 1674$.

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Antonio Linero-Bas, Daniel Nieves-Roldán. 2021-08-02. The maximum of the complementary of a semigroup with restricted conditions. https://arxiv.org/abs/2108.02004

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