A Lower Bound for the Size of a Sum of Dilates

2011/01/28 by Željka Ljujić, Zeljka Ljujic, Ljujic, Zeljka
Mathematics · #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT) #math.CO #math.NT

paper · pdf · doi:10.48550/arxiv.1101.5425

v2 Case $k=pq$ added

openalex publication_date 2011/01/28 · arxiv created 2011/03/14 · arxiv updated 2011/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A be a subset of integers and let 2⋅ A+k⋅ A=\2a₁+ka₂ : a₁,a₂∈ A\. Y. O. Hamidoune and J. Ru' e proved that if k is an odd prime and A a finite set of integers such that |A|>8k^k, then |2⋅ A+k⋅ A|≥ (k+2)|A|-k²-k+2. In this paper, we extend this result for the case when k is a power of an odd prime and the case when k is a product of two odd primes.

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