On the Exponential Diophantine Equation
نویسنده
چکیده
Let a, b, c be fixed positive integers satisfying a2 + ab + b2 = c with gcd(a, b) = 1. We show that the Diophantine equation a2x+axby+b2y = cz has only the positive integer solution (x, y, z) = (1, 1, 1) under some conditions. The proof is based on elementary methods and Cohn’s ones concerning the Diophantine equation x2 + C = yn. Mathematics Subject Classification: 11D61
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