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On The Diophantine Equation <i>x<sup>a</sup></i> + <i>y<sup>a</sup> </i>= <i>p<sup>k</sup>z<sup>b</sup></i>
In this study, we consider the Diophantine equation xa + ya = pkzb where p is a prime number, gcd(a, b) = 1 and k,a,b∈Z+. We solve this equation parametrically by considering different cases of x and y and find that there exist infinitely many nontrivial integer solutions, where the …