On sums of dilates

Javier, Cilleruelo; Hamidoune, Yahya Ould; Serra Albó, Oriol

doi:10.1017/S0963548309990307

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Javier, Cilleruelo

Hamidoune, Yahya Ould

Serra Albó, Oriol

Document typeArticle

Defense date2009-10-05

Rights accessOpen Access

Except where otherwise noted, content on this work is licensed under a Creative Commons license : Attribution-NonCommercial-NoDerivs 3.0 Spain

Abstract

For k prime and A a finite set of integers with |A| ≥ $3(k-1)^2$ (k-1)! we prove that |A+k·A| ≥ (k+1)|A| − ⌈k(k+2)/4⌉ where k·A = {ka:a∈A}. We also describe the sets for which equality holds.

CitationJavier, C.; O. Hamidoune, Y.; Serra, O. On sums of dilates. "Combinatorics probability and computing", 05 Octubre 2009, vol. 18, núm. 6, p. 871-880.

URIhttp://hdl.handle.net/2117/11654

DOI10.1017/S0963548309990307

ISSN0963-5483

Publisher versionhttp://journals.cambridge.org/action/displayJournal?jid=CPC

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