On the critical pair theory in Z/pZ

Details On the critical pair theory in Z/pZ On the critical pair theory in Z/pZ

2005-07-27

arxiv.org/abs/math/0507561v1

Acta Arithmetica, 121.2 (2006) pp. 99--115.

Mathematics

Number Theory

21 pages, submitted to Acta Arithmetica

Scientific paper

Let A and B be subsets of Z/pZ such that |A+B| < |A|+|B|+2. We prove that, if
|A|>3, |B|>4, |A+B| 52, then A and B are included in arithmetic
progressions with the same difference and of size |A|+2 and |B|+2 respectively.
This extends the well-known theorem of Vosper and a recent result of Rodseth
and one of the present authors.

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