This article is cited in 1 paper

Multiplicative decomposition of arithmetic progressions in prime fields

M. Z. Garaev^a, S. V. Konyagin<sup>b

a</sup> Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Morelia 58089, Michoacán, Mexico
^b Steklov Mathematical Institute, 8 Gubkin Street, Moscow 119991, Russia

Abstract: We prove that there exists an absolute constant $c>0$ such that if an arithmetic progression $\mathcal{P}$ 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 $\mathcal{P}=-\mathcal{P}$ or $\mathcal{P}=\{-2r,r,4r\}$ for some residue $r$ modulo $p$.

Received: 26.09.2013
Revised: 23.05.2014
Accepted: 09.06.2014

Language: English

DOI: 10.1016/j.jnt.2014.06.011

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