Geodesic
On the sum of dilations of a set
Antal Balog 1   ; George Shakan 2
1 Alfréd Rényi Institute of Mathematics P.O. Box 127 1364 Budapest, Hungary
2 Department of Mathematics University of Wyoming Laramie, WY 82072, U.S.A.
Acta Arithmetica, Tome 164 (2014) no. 2, pp. 153-162 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that for any relatively prime integers $1\leq p q$ and for any finite $A \subset \mathbb {Z}$ one has $$|p \cdot A + q \cdot A | \geq (p + q) |A| - (pq)^{(p+q-3)(p+q) + 1}.$$
DOI : 10.4064/aa164-2-5
Keywords: relatively prime integers leq finite subset mathbb has cdot cdot geq q

Antal Balog  1   ; George Shakan  2

1 Alfréd Rényi Institute of Mathematics P.O. Box 127 1364 Budapest, Hungary
2 Department of Mathematics University of Wyoming Laramie, WY 82072, U.S.A. 
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Antal Balog; George Shakan. On the sum of dilations of a set. Acta Arithmetica, Tome 164 (2014) no. 2, pp. 153-162. doi: 10.4064/aa164-2-5

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