Note on a problem of Sárközy on multiplicative representation functions

2025/04/13 by Yuchen Ding, Ding, Yuchen
Mathematics · #Mathematical Analysis and Transform Methods #Analytic Number Theory Research #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2504.09545

Abstract

Motivated by a 2001 problem of Sárközy, we classify all situations of the integers b,c,e and f satisfying \limsup_n→∞|d(A,bn+c)-d(A,en+f)|=∞ for any infinite A⊂ ℕ, where d(A,m)=#\a∈ A:a|m\.

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