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On Sums of Dilates
JAVIER CILLERUELO, YAHYA O. HAMIDOUNE, ORIOL SERRA
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Source: Crossref
Published: Jul 9, 2009
DOI: 10.1017/s0963548309990307
Open original source ↗Source 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.
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