# Bicyclotomic polynomials and impossible intersections

@article{Masser2013BicyclotomicPA,
title={Bicyclotomic polynomials and impossible intersections},
author={David Masser and Umberto Zannier},
journal={Journal de Theorie des Nombres de Bordeaux},
year={2013},
volume={25},
pages={635-659}
}
• Published 2013
• Mathematics
• Journal de Theorie des Nombres de Bordeaux
In a recent paper we proved that there are at most finitely many complex numbers t 6= 0, 1 such that the points (2, √ 2(2− t)) and (3, √ 6(3− t)) are both torsion on the Legendre elliptic curve defined by y2 = x(x − 1)(x − t). In a sequel we gave a generalization to any two points with coordinates algebraic over the field Q(t) and even over C(t). Here we reconsider the special case (u, √ u(u− 1)(u− t)) and (v, √ v(v − 1)(v − t)) with complex numbers u and v.
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