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On the critical pair theory in Z/pZ

Yahya Ould Hamidoune·Oriol Serra·Gilles Zemor
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Abstract

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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Yahya Ould Hamidoune, Oriol Serra, Gilles Zemor. 2005-07-27. On the critical pair theory in Z/pZ. https://arxiv.org/abs/math/0507561

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