Powers in Lucas Sequences via Galois Representations

Jesse Silliman; Isabel Vogt

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arXiv · 1307.5078

Powers in Lucas Sequences via Galois Representations

Jesse Silliman·Isabel Vogt

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Abstract

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.

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Jesse Silliman, Isabel Vogt. 2013-07-24. Powers in Lucas Sequences via Galois Representations. https://arxiv.org/abs/1307.5078

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