Covering shrinking polynomials by quasi progressions

2023/02/01 by Hegyvári, Norbert
#11B13 #11B75 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.00408

Abstract

Erd\H os introduced the quantity S=T∑^T_i=1X_i, where X₁,…, X_T are arithmetic progressions, and cover the square numbers up to N. He conjectured that S is close to N, i.e. the square numbers cannot be covered "economically" by arithmetic progressions. Sárközy confirmed this conjecture and proved that S≥ cN/log²N. In this paper, we extend this to shrinking polynomials and so-called \X_i\ quasi progressions.

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