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24 June 2024
 
  » arxiv » 2302.00408

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Covering shrinking polynomials by quasi progressions
Norbert Hegyvári ;
Date 1 Feb 2023
AbstractErdH os introduced the quantity $S=Tsum^T_{i=1}X_i$, where $X_1,dots, X_T$ 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. S’ark"ozy confirmed this conjecture and proved that $Sgeq cN/log^2N$. In this paper, we extend this to shrinking polynomials and so-called ${X_i}$ quasi progressions.
Source arXiv, 2302.00408
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