Prime power terms in elliptic divisibility sequences

TL;DR

This paper investigates prime power terms in elliptic divisibility sequences, relating the problem to classical diophantine geometry, and provides explicit bounds on their indices when descent via isogeny is possible.

Contribution

It introduces a method to explicitly bound the indices of prime power terms in elliptic divisibility sequences using isogeny descent techniques.

Findings

Explicit upper bounds on prime power term indices in elliptic divisibility sequences

Connection established between prime power terms and classical diophantine problems

Method applicable to sequences derived from elliptic curves with isogeny descent

Abstract

We consider a particular case of an analog for elliptic curves to the Mersenne problem : finding explicitely all prime power terms in an elliptic divisibility sequence when descent via isogeny is possible. We explain how this question can be related to classical problems in diophantine geometry and we compute an explicit upper bound on the index of prime power terms in magnified elliptic divisibility sequences.