Prime power terms in elliptic divisibility sequences

Mahé, Valéry

doi:10.1090/S0025-5718-2013-02790-1

Prime power terms in elliptic divisibility sequences
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Math. Comp. 83 (2014), 1951-1991 Request permission

Abstract:

We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic divisibility sequences associated to points in the image of a nontrivial isogeny. We also discuss the uniformity of these bounds assuming the Hall–Lang conjecture.

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