Let E/ℚ be an elliptic curve. Silverman and Stange define primes p and q to be an elliptic, amicable pair if #E(Fp) = q and #E(Fq) = p. More generally, they define the notion of aliquot cycles for elliptic curves. Here, we study the same notion in the case that the elliptic curve is defined over a number field K. We focus on proving the existence of an elliptic curve E/K with aliquot cycle (p1,⋯, pn) where the pi are primes of K satisfying mild conditions.
| Identifer | oai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-16327 |
| Date | 01 January 2016 |
| Creators | Brown, Jim, Heras, David, James, Kevin, Keaton, Rodney, Qian, Andrew |
| Publisher | Digital Commons @ East Tennessee State University |
| Source Sets | East Tennessee State University |
| Detected Language | English |
| Type | text |
| Source | ETSU Faculty Works |
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