Page 1 Next

Displaying 1 – 20 of 172

Showing per page

Arithmetic progressions in sumsets

Imre Z. Ruzsa (1991)

Acta Arithmetica

1. Introduction. Let A,B ⊂ [1,N] be sets of integers, |A|=|B|=cN. Bourgain [2] proved that A+B always contains an arithmetic progression of length e x p ( l o g N ) 1 / 3 - ε . Our aim is to show that this is not very far from the best possible. Theorem 1. Let ε be a positive number. For every prime p > p₀(ε) there is a symmetric set A of residues mod p such that |A| > (1/2-ε)p and A + A contains no arithmetic progression of length (1.1) e x p ( l o g p ) 2 / 3 + ε . A set of residues can be used to get a set of integers in an obvious way. Observe...

Currently displaying 1 – 20 of 172

Page 1 Next