Open AccessA note on the Diophantine Equation x^2-kxy+ky^2+ly=0
Author(s) -
Sakha A. Alkabouss,
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Boualem Benseba,
Nacira Berbara,
Simon Earp-Lynch,
Florian Luca,
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Publication year - 2021
Publication title -
mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.294
H-Index - 6
eISSN - 2601-744X
pISSN - 1222-9016
DOI - 10.24193/mathcluj.2021.2.01
Subject(s) - diophantine equation , mathematics , legendre's equation , diophantine set , characterization (materials science) , thue equation , discrete mathematics , pure mathematics , physics , optics
We investigate the Diophantine equation x^2 −kxy + ky^2 + ly = 0 for integers k and l with k even. We give a characterization of the positive solutions of this equation in terms of k and l. We also consider the same equation for other values of k and l.