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Mathematics > Number Theory

arXiv:1001.5303 (math)
[Submitted on 29 Jan 2010]

Title:Terms in elliptic divisibility sequences divisible by their indices

Authors:Katherine E. Stange, Joseph H. Silverman
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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.
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: Primary: 11G05, Secondary: 11B37, 11G20, 14G25
Cite as: arXiv:1001.5303 [math.NT]
  (or arXiv:1001.5303v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1001.5303
Journal reference: Acta Arith. 146.4 (2011), 355--378
Related DOI: https://doi.org/10.4064/aa146-4-4

Submission history

From: Joseph H. Silverman [view email]
[v1] Fri, 29 Jan 2010 20:40:13 UTC (24 KB)
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