Type: Article

Multiplicative decomposition of arithmetic progressions in prime fields

Garaev, M. Z.; Konyagin, S. V;

Abstract:

We prove that there exists an absolute constant c > 0 such that if an arithmetic progression P modulo a prime number p does not contain zero and has the cardinality less than cp, then it cannot be represented as a product of two subsets of cardinality greater than 1, unless P = -P or P = {-2r, r, 4r} for some residue r modulo p.