Covering an arithmetic progression with geometric progressions and vice versa
نویسندگان
چکیده
منابع مشابه
Arithmetic and Geometric Progressions in Productsets over Finite Fields
Given two sets A,B ⊆ IFq of elements of the finite field IFq of q elements, we show that the productset AB = {ab | a ∈ A, b ∈ B} contains an arithmetic progression of length k ≥ 3 provided that k < p, where p is the characteristic of IFq, and #A#B ≥ 3q 2d−2/k. We also consider geometric progressions in a shifted productset AB + h, for f ∈ IFq, and obtain a similar result.
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ژورنال
عنوان ژورنال: International Journal of Number Theory
سال: 2014
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042114500456