The support problem and its elliptic analogue

[摘要] Let F be a number field, Suppose x, y is an element of F* have the property that for all n is an element of Z and almost all prime ideals p of the ring of integers of F* one has that y(n) = 1 (mod p) whenever x(n) = 1 (mod p). We show that then y is a power of x. This answers a question of Erdos. We also prove an elliptic analogue of this result. (C) 1997 Academic Press.

[发布日期] 1997-06-01