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.
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Arif S. A., 1998, INT J MATH MATH SCI, V21, P619, DOI DOI 10.1155/S0161171298000866