Amicable Pairs and Aliquot Cycles for Elliptic Curves

DOI10.1080/10586458.2011.565253zbMath1269.11056arXiv0912.1831OpenAlexW2065422049WikidataQ110479318 ScholiaQ110479318MaRDI QIDQ4915396

Katherine E. Stange, Joseph H. Silverman

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1831

zbMATH Keywords

elliptic curveelliptic divisibility sequencealiquot cycleamicable pair

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Curves over finite and local fields (11G20) Special sequences and polynomials (11B83)

Related Items (10)

"Equation missing" -Integral Points on a Mordell Curve ⋮ Sums of Euler products and statistics of elliptic curves ⋮ Amicable pairs and aliquot cycles on average ⋮ A survey of elliptic curves for proof systems ⋮ Scalable zero knowledge via cycles of elliptic curves ⋮ Revisiting cycles of pairing-friendly elliptic curves ⋮ Computing integral points on hyperelliptic curves using quadratic Chabauty ⋮ An asymptotic for the average number of amicable pairs for elliptic curves ⋮ Amicable pairs and aliquot cycles for elliptic curves over number fields ⋮ On Cycles of Pairing-Friendly Elliptic Curves

Uses Software

• PARI/GP

Cites Work

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• Reductions of an elliptic curve with almost prime orders

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