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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 $x, y \geq 1$ , $α, β, γ, n \geq 3$ with $gcd (x, y) = 1$ .

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On the Diophantine equation x 2 + 2 α 5 β 17 γ = y n

On the Diophantine equation $x^{2} + 2^{α} 5^{β} 17^{γ} = y^{n}$