### Perfect powers in elliptic divisibility sequences

Linfoot Number Theory Seminar

8th May 2024, 11:00 am – 12:00 pm

Fry Building, 2.04

Let E be an elliptic curve over the rationals given by an integral Weierstrass model and let P be a rational point of infinite order. The multiple nP has the form (A_n/B_n^2,C_n/B_n^3) where A_n, B_n, C_n are integers with A_nC_n and B_n coprime, and B_n positive. The sequence (B_n) is called the elliptic divisibility sequence generated by P. In this talk we answer the question posed in 2007 by Everest, Reynolds and Stevens: does the sequence (B_n) contain only finitely many perfect powers?

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