Large gaps between sums of two squareful numbers

2023/03/26 by Alexander Kalmynin, Kalmynin, Alexander, Segei Konyagin +1
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2303.14833

Abstract

Let M(x) be the length of the largest subinterval of [1,x] which does not contain any sums of two squareful numbers. We prove a lower bound M(x)≫ (ln x)/((lnln x)²) for all x≥ 3. The proof relies on properties of random subsets of the prime numbers.

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