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arXiv · 2403.07534

Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version)

Takao Komatsu·Neha Gupta·Manoj Upreti
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Abstract

We give an explicit formula for the $p$-Frobenius number of triples associated with Diophantine equations $x^2+y^2=z^r$, that is, the largest positive integer that can only be represented in $p$ ways by combining the three integers of the solutions of Diophantine equations $x^2+y^2=z^r$. When $r=2$, the Frobenius number has already been given.

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Takao Komatsu, Neha Gupta, Manoj Upreti. 2024-03-12. Frobenius numbers associated with Diophantine triples of $x^2+y^2=z^r$ (extended version). https://arxiv.org/abs/2403.07534

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