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Frobenius Numbers Associated with Diophantine Triples of x2-y2=zr
- Source :
- Symmetry, Vol 16, Iss 7, p 855 (2024)
- Publication Year :
- 2024
- Publisher :
- MDPI AG, 2024.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 20738994
- Volume :
- 16
- Issue :
- 7
- Database :
- Directory of Open Access Journals
- Journal :
- Symmetry
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.238dab33db92483db8485a80de309e19
- Document Type :
- article
- Full Text :
- https://doi.org/10.3390/sym16070855