Geodesic
Integer solutions of the equation \(y^2 = Ax^4 + B\)
Journal of integer sequences, Tome 18 (2015) no. 4
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 
@article{JIS_2015__18_4_a4,
     author = {Alvanos,  Paraskevas K. and Draziotis,  Konstantinos A.},
     title = {Integer solutions of the equation \(y^2 = {Ax^4} + {B\)}},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {4},
     zbl = {1378.11042},
     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/