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J. Number Theory, 2014, Volume 145, Pages 540–553 (Mi jnt3)  

Multiplicative decomposition of arithmetic progressions in prime fields

M. Z. Garaeva, S. V. Konyaginb

a 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 $p$.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00332
Ministry of Education and Science of the Russian Federation Nsh-3082.2014.1
Direccion General de Asuntos del Personal Academico, Universidad Nacional Autonoma de Mexico
The first author was supported by the sabbatical grant from PASPA-DGAPA-UNAM. The second author was supported by Russian Foundation for Basic Research, Grant No. 14-01-00332, and Program Supporting Leading Scientific Schools, Grant Nsh-3082.2014.1.


DOI: https://doi.org/10.1016/j.jnt.2014.06.011


Bibliographic databases:

Document Type: Article
Received: 26.09.2013
Revised: 23.05.2014
Accepted:09.06.2014
Language: English

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