TY  - JOUR
AU  - Wong, Keng Yarn 
AU  - Kamarulhaili, Hailiza 
PY  - 2017
TI  - On The Diophantine Equation xa + ya = pkzb
JF  - Journal of Mathematics and Statistics
VL  - 13
IS  - 1
DO  - 10.3844/jmssp.2017.38.45
UR  - https://thescipub.com/abstract/jmssp.2017.38.45
AB  - 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.