On a problem of Graham

Abstract

p non-zero residues (mod p) . Assume that if ' a i a i , ei=0 or 1 (not all e i=0) is a i=1 p multiple of p then is uniquely determined . The conjecture states that in this i=1 case there are only two distinct residues among the a's . We are going to prove this conjecture for all sufficiently large p, in fact we will prove a sharper result . To extend our proof for the small values of p would require considerable computation, but no theoretical difficulty . Our proof is surprisingly complicated and we are not convinced that a simpler proof is not possible, but we could not find one . First we prove

Cite this paper

@inproceedings{Erds2004OnAP, title={On a problem of Graham}, author={Edina Erdős and Endre Szemer{\'e}di}, year={2004} }