In this paper, we study the Diophantine equation a^x+(a+5b)^y=z^2 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 p^x+(p+5a)^y=z^2 where p and p+5a are both primes and p≡ 1( 5) and a is a positive integer.
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Dokchan et al. (2024) studied this question.
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