Amicable Pairs and Aliquot Cycles for Elliptic Curves over Number Fields
نویسندگان
چکیده
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.
منابع مشابه
Amicable Pairs and Aliquot Cycles for Elliptic Curves
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