The Support Problem and Its Elliptic Analogue Original Research Article

LetFbe a number field, Supposex, yset membership, variantF* have the property that for allnset membership, variantZand almost all prime ideals image of the ring of integers ofF* one has thatyn≡1 (mod image) wheneverxn≡1 (mod image). We show that thenyis a power ofx. This answers a question of Erdimages. We also prove an elliptic analogue of this result.