  In this note we consider the title Diophantine equation from both theoretical
as well as experimental point of view. In particular, we prove that for $k=4,
6$ and each choice of the signs our equation has infinitely many co-prime
positive integer solutions. For $k=5, 7$ and all choices of the signs we
computed all co-prime positive integer solutions $(x, y, a, b)$ satisfying the
condition $\op{max}\{a, b\}\leq 50000$.
