On Non-intersecting Arithmetic Progressions

Details On Non-intersecting Arithmetic Progressions On Non-intersecting Arithmetic Progressions

2002-08-30

arxiv.org/abs/math/0208236v1

Mathematics

Combinatorics

Submitted

Scientific paper

We prove that if one has k non-intersecting arithmetic progressions of
integers, with common differences 2 <= q_1,...,q_k <= x, then k < x exp((-1/6 +
o(1)) sqrt(log x loglog x)). This improves a result of Szemeredi and Erdos.

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