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On The Integer Solutions of the Diophantine Equations x2+ay2 = zn
Current Issue
Volume 4, 2016
Issue 2 (April)
Pages: 9-16   |   Vol. 4, No. 2, April 2016   |   Follow on         
Paper in PDF Downloads: 66   Since Jul. 19, 2016 Views: 1446   Since Jul. 19, 2016
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
Reference
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Cihangir, A. and Şenay, H.; On the Integer Solutions of The Diophantine Equations x2+y2=z2 and xn+y2=z2, Jour. of. Math.& Comp.Sci (Math.Ser.) 2002;15(2):79–84.
[15]
Cihangir A; (1998), Pythagorean Üçlüleri Grubu ile z2-ay2=x2 Denkleminin Çözüm Üçlüleri Kümesinin Cebirsel Özellikleri ve xp+ay2=zq Diophantine Denkleminin Tamsayı Çözümleri Üzerine, Ph.D. Thesis, S.Ü. Fen Bilimleri Enstitüsü–Konya, Turkey.
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