[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.
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.
Exponential Diophantine Equations, Pythagorean Triangles, Higher Degree Equations
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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.
