Jesse Silliman, Isabel Vogt
Published 2013-07-18, updated 2013-07-24Version 2
Let $u_n$ be a nondegenerate Lucas sequence. We generalize the results of Bugeaud, Mignotte, and Siksek, 2006 to give a systematic approach towards the problem of determining all perfect powers in any particular Lucas sequence. We then prove a general bound on admissible prime powers in a Lucas sequence assuming the Frey-Mazur conjecture on isomorphic mod $p$ Galois representations of elliptic curves.
Integral points on elliptic curves and 3-torsion in class groups
Thue equations and torsion groups of elliptic curves
On Elkies subgroups of l-torsion points in elliptic curves defined over a finite field
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