On The Diophantine Equation {formula}

摘要

In this paper, we consider the Diophantine equation {formula}, where a, b, k are positive integers, (a,b) = 1, m and p are primes and x_1, x_2, ..., x_m, y are integers with x_1 = x_2 = ... = x_m. We solve this equation parametrically by considering two different cases depending on prime numbers m and p where m = p or m + p.