Terms in elliptic divisibility sequences divisible by their indices

Details Terms in elliptic divisibility sequences divisible by their indices Terms in elliptic divisibility sequences divisible by their indices

2010-01-29

arxiv.org/abs/1001.5303v1

Acta Arith. 146.4 (2011), 355--378

Mathematics

Number Theory

Scientific paper

Let D = (D_n)_{n\ge1} be an elliptic divisibility sequence. We study the set S(D) of indices n satisfying n | D_n. In particular, given an index n in S(D), we explain how to construct elements nd in S(D), where d is either a prime divisor of D_n, or d is the product of the primes in an aliquot cycle for D. We also give bounds for the exceptional indices that are not constructed in this way.

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