On the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn
نویسندگان
چکیده
In this paper, we find all the solutions of the Diophantine equation x + 2 513 = y in nonnegative integers x, y, α, β, γ, n ≥ 3 with x and y coprime. In fact, for n = 3, 4, 6, 8, 12, we transform the above equation into several elliptic equations written in cubic or quartic models for which we determine all their {2, 5, 13}-integer points. For n ≥ 5, we apply a method that uses primitive divisors of Lucas sequences. Again we are able to obtain several elliptic equations written in cubic models for which we find all their {2, 5, 13}-integer points. All the computations are done with MAGMA [12].
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