Abstract
Cohn(2) has solved the title equation in the case k = 0. Our object here is to generalize his result for all k greater than or equal to 0, and to prove
Theorem
The diophantine equation x(2) + 5(2k+1) = y(n), n greater than or equal to 3, has no solution in integers x, y for all k greater than or equal to 0.