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arXiv · 1001.5303

Terms in elliptic divisibility sequences divisible by their indices

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.

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Katherine E. Stange, Joseph H. Silverman. 2010-01-29. Terms in elliptic divisibility sequences divisible by their indices. https://doi.org/10.4064/aa146-4-4

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