Arithmetic and Geometric Progressions in Productsets over Finite Fields

Details Arithmetic and Geometric Progressions in Productsets over Finite Fields Arithmetic and Geometric Progressions in Productsets over Finite Fields

2007-11-12

arxiv.org/abs/0711.1800v2

Mathematics

Number Theory

Scientific paper

Given two sets $\cA, \cB \subseteq \F_q$ of elements of the finite field $\F_q$ of $q$ elements, we show that the productset $$ \cA\cB = \{ab | a \in \cA, b \in\cB\} $$ contains an arithmetic progression of length $k \ge 3$ provided that $k

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