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On The Integer Solutions of the Diophantine Equations x2+ay2 = zn
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Volume 4, 2016
Issue 2 (April)
Pages: 9-16   |   Vol. 4, No. 2, April 2016   |   Follow on
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Authors
[1]
Ahmet Cihangir, Elementary Mathematics Education Programme, Ahmet Kelesoglu Education Faculty, Necmettin Erbakan University, Konya, Turkey.
[2]
Hasan Şenay, Elementary Mathematics Education Programme, Faculty of Education, Mevlana University, Konya, Turkey.
Abstract
In this study; where the variables x, y and z are integers, a and n positive integers, existence of x, y, z integer solutions’ for each positive n integers of x2+ay2 = zn Diophantine equation was shown by induction. Also change of z was analyzed according to the values which a will take and each situation was exemplified.
Keywords
Exponential Diophantine Equations, Pythagorean Triangles, Higher Degree Equations
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