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In this paper, we study the Diophantine equation aˣ+ (a+5b) ʸ=z² when a 1 (5) and b is a positive integer. We establish that the equation has no solutions in positive integers x, y and z. We start with the Diophantine equation pˣ+ (p+5a) ʸ=z² where p and p+5a are both primes and p 1 (5) and a is a positive integer.
Dokchan et al. (Thu,) studied this question.
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