On the Diophantine Equation (p+12)x+(p+2k)y=z2 where p is a Prime Number

Abstract

In this paper, we consider the Diophantine equation (P+ 12) X+ (P+2K)=Z2where p > 3, p are primes and k is natural number, when x, y and z are non-negative integers. It is found that the Diophantine equation has no nonnegative integer solution.