The p-Frobenius Problems for the Sequence of Generalized Repunits

Komatsu, Takao; Laohakosol, Vichian

doi:10.1007/s00025-023-02055-6

Results Math

2023

DOI: 10.1007/s00025-023-02055-6

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The p-Frobenius Problems for the Sequence of Generalized Repunits

Takao Komatsu,

Vichian Laohakosol

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2024

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Cited by 1 publication

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Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr

Yin,

Komatsu

2024

Symmetry

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We give an explicit formula for the p-Frobenius number of triples associated with Diophantine Equations x2−y2=zr (r≥2), 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 x2−y2=zr. This result is also a generalization because if r=2 and p=0, the (0-)Frobenius number of the Pythagorean triple has already been given. To find p-Frobenius numbers, we use geometrically easy to understand figures of the elements of the p-Apéry set, which exhibits symmetric appearances.

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Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr

Yin,

Komatsu

2024

Symmetry

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show abstract

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The p-Frobenius Problems for the Sequence of Generalized Repunits

Cited by 1 publication

References 14 publications

Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr

Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr

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