Terms in elliptic divisibility sequences divisible by their indices

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.

Cited by in corpus (5)

• Amicable pairs and aliquot cycles for elliptic curves
• Algebraic divisibility sequences over function fields
• Integral points on elliptic curves and explicit valuations of division polynomials
• Greatest common divisors of shifted primes and Fibonacci numbers
• Elliptic Fermat numbers and elliptic divisibility sequence