Shifted powers in Lucas-Lehmer sequences

Bennett, Michael A. ✉; Patel, Vandita; Siksek, Samir

Angol nyelvű Tudományos Szakcikk (Folyóiratcikk)
Megjelent: RESEARCH IN NUMBER THEORY 2363-9555 5 (1) Paper: 15 , 27 p. 2019
  • SJR Scopus - Algebra and Number Theory: Q1
    We develop a general framework for finding all perfect powers in sequences derived via shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to answer a question of Bugeaud, Luca, Mignotte and the third author by explicitly finding all perfect powers of the shape F-k +/- 2 where F-k is the k-th term in the Fibonacci sequence.
    Hivatkozás stílusok: IEEEACMAPAChicagoHarvardCSLMásolásNyomtatás
    2021-05-10 20:29