Perfect powers in elliptic divisibility sequences

Details Perfect powers in elliptic divisibility sequences Perfect powers in elliptic divisibility sequences

2011-01-15

arxiv.org/abs/1101.2949v2

Mathematics

Number Theory

16 pages

Scientific paper

It is shown that there are finitely many perfect powers in an elliptic divisibility sequence whose first term is divisible by 2 or 3. For Mordell curves the same conclusion is shown to hold if the first term is greater than 1. Examples of Mordell curves and families of congruent number curves are given with corresponding elliptic divisibility sequences having no perfect power terms. The proofs combine primitive divisor results with modular methods for Diophantine equations.

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