@article {10.3844/jmssp.2017.38.45,
article_type = {journal},
title = {On The Diophantine Equation xa + ya = pkzb},
author = {Wong, Keng Yarn and Kamarulhaili, Hailiza},
volume = {13},
year = {2017},
month = {Mar},
pages = {38-45},
doi = {10.3844/jmssp.2017.38.45},
url = {https://thescipub.com/abstract/jmssp.2017.38.45},
abstract = {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 formulated parametric solutions solve xa + ya = pkzb completely for the case of x = y, x = −y, and either x or y is zero (not both zero). For the case of |x| ≠ |y| and both x and y nonzero, not every solution (x,y,z) is in the parametric forms proposed in Theorem 5, although any (x,y,z) in these parametric forms solves the Diophantine equation.},
journal = {Journal of Mathematics and Statistics},
publisher = {Science Publications}
}