Geodesic
Integer solutions of the equation $y^2 = Ax^4 + B$
Journal of integer sequences, Tome 18 (2015) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Let $A \in {k^{2}(k^{2}l^{2} + 1), 4k^{2}(k^{2}(2l - 1)^{2} + 1)}$, where $k$ and $l$ are positive integers, and let $B$ be a non-zero square-free integer such that $|B| \sqrt A$. In this paper we determine all the possible integer solutions of the equation $y^{2} = Ax^{4} + B$ by using terms of Lucas sequences of the form $mx^{2}$.
Classification : 11D25, 11D41, 11A55, 11B39
Keywords: Lucas sequence, continued fraction, Diophantine equation, quartic elliptic curve 
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     author = {Alvanos, Paraskevas K. and Draziotis, Konstantinos A.},
     title = {Integer solutions of the equation $y^2 = Ax^4 + B$},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_4_a4/}
}
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Alvanos, Paraskevas K.; Draziotis, Konstantinos A. Integer solutions of the equation $y^2 = Ax^4 + B$. Journal of integer sequences, Tome 18 (2015) no. 4. http://geodesic.mathdoc.fr/item/JIS_2015__18_4_a4/