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Research articles

ScienceAsia 46 (2020): 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 x2x yy2 ± l x = 0 and x23x y + y2 ± l x = 0, where l is of the form mn 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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a 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