On the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn

@inproceedings{Goins2008OnTD,
  title={On the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn},
  author={Edray Goins and Florian Luca and Alain Togb{\'e}},
  year={2008}
}
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… CONTINUE READING

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On the equation x 2 + 5 a · 13 b = y n

F. S. Abu Muriefah, F. Luca, A. Togbé
Glasgow J . Math . • 2008

On the equation x2 + 5 · 13 = y

F. S. Abu Muriefah, F. Luca, A. Togbé
Glasgow J. Math. 50, 143–161 • 2008
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F. Luca, A. Togbé
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On the diophantine equation x2 + 2 · 3 · 5 · 7 = y

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Publ. Math. Debrecen 70, 149–166 • 2006
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On the diophantine equation x2 + 5 = y

F. S. Abu Muriefah
Demonstratio Mathematica 319(2), 285–289 • 2006

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