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Asymptotic number of solutions of some systems of diophantine inequalities

✍ Scribed by V. I. Bernik


Publisher
SP MAIK Nauka/Interperiodica
Year
1972
Tongue
English
Weight
179 KB
Volume
11
Category
Article
ISSN
0001-4346

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Solutions of some quadratic Diophantine
✍ Refik Keskin πŸ“‚ Article πŸ“… 2010 πŸ› Elsevier Science 🌐 English βš– 249 KB

In this study, we investigate positive integer solutions of the Diophantine equations x 2 -kxyβˆ“y 2 βˆ“x = 0 and x 2 -kxy-y 2 βˆ“y = 0. It is shown that when k > 3, x 2 -kxy+y 2 +x = 0 has no positive integer solutions but the equation x 2 -kxy + y 2 -x = 0 has positive integer solutions. Moreover, it is