On the Diophantine equation x 2 + 2 α 5 β 17 γ = y n Hemar Godinho; Diego Marques; Alain Togbé — 2012 Communications in Mathematics In this paper, we find all solutions of the Diophantine equation x 2 + 2 α 5 β 17 γ = y n in positive integers x , y ≥ 1 , α , β , γ , n ≥ 3 with gcd ( x , y ) = 1 .