On the diophantine equations x2 + 74 = y5 and x2 + 86 = y5

Abstract

J. H. E. Cohn solved the diophantine equations x2 + 74 = yn and x2 + 86 = yn, with the condition 5 ∤ n, by more or less elementary methods. We complete this work by solving these equations for 5 | n, by less elementary methods.