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arXiv · 2309.09149

Generalized Frobenius Number of Three Variables

Kittipong Subwattanachai
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Abstract

For $ k \geq 2 $, we let $ A = (a_{1}, a_{2}, \ldots, a_{k}) $ be a $k$-tuple of positive integers with $\gcd(a_{1}, a_2, \ldots, a_k) =1$ and, for a non-negative integer $s$, the generalized Frobenius number of $A$, $g(A;s) = g(a_1, a_2, \ldots, a_k;s)$, the largest integer that has at most $s$ representations in terms of $a_1, a_2, \ldots, a_k$ with non-negative integer coefficients. In this article, we give a formula for the generalized Frobenius number of three positive integers $(a_1,a_2,a_3)$ with certain conditions.

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Kittipong Subwattanachai. 2023-09-17. Generalized Frobenius Number of Three Variables. https://arxiv.org/abs/2309.09149

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