The Support Problem and Its Elliptic Analogue

Abstract

Let F be a number field, Suppose x, y Є F* have the property that for all n Є Z and almost all prime ideals p of the ring of integers of F* one has that yn =1 (mod p) whenever xn=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.