Terms in elliptic divisibility sequences divisible by their indices
Number Theory
2014-12-30 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1001.5303,
title = {Terms in elliptic divisibility sequences divisible by their indices},
author = {Katherine E. Stange and Joseph H. Silverman},
journal= {arXiv preprint arXiv:1001.5303},
year = {2014}
}