Research articles
ScienceAsia 46 (2020):ID 490-493 |doi:
10.2306/scienceasia1513-1874.2020.058
On the Diophantine equations x2-xy-y2+lx=0
and x2-3xy+y2+lx=0
Yaowaluk Alibaud, Supawadee Prugsapitak*, Wuttichon Aukkhosuwan
ABSTRACT: This study determines all positive integer solutions of the Diophantine equations of the form x2 − x y −
y2 ± l x = 0 and x2 − 3x y + y2 ± l x = 0, where l is of the form m∏n i=1 piai , pi is a prime congruent to 2 or 3 modulo 5,
and m is either 1 or 5. In addition, we also provide all positive integer solutions of x2 − x y − y2 ± l y = 0.
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Algebra and Applications Research Unit, Department of Mathematics and Statistics, Faculty of Science,
Prince of Songkla University, Songkhla 90110 Thailand |
* Corresponding author, E-mail: supawadee.p@psu.ac.th
Received 18 Apr 2020, Accepted 16 Jun 2020
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