Corrales Rodrigáñez, CarmenSchoof, René2023-06-202023-06-201997J. W. S. Cassels and A. Frohlich, Eds., ``Algebraic Number Theory,'' Academic Press,London/New York, 1967. G. Janusz, ``Algebraic Number Theory,'' Academic Press, New York/London, 1973. J. Silverman, ``The Arithmetic of Elliptic Curves,''Graduate Texts in Mathematics,Vol. 106, Springer-Verlag, Heidelberg/New York, 1986. A. Schinzel, On exponential congruences, Mat. Zametki, to appear. J.-P. Serre, Proprietes galoisiennes des points d'ordre fini des courbes elliptiques, Invent.Math. 15 (1972),259-331. (1uvres, III, Springer-Verlag, Berlin/Heidelberg/New York/Tokyo, 1986, 1-73.)1096-165810.1006/jnth.1997.2114https://hdl.handle.net/20.500.14352/58330Let 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022314X97921144http://www.sciencedirect.comrestricted access511Algebraic numberCongruenceSupport problemElliptic curvesTeoría de números1205 Teoría de Números