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arXiv · 2303.14833

Large gaps between sums of two squareful numbers

Alexander Kalmynin·Sergei Konyagin
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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 \[ M(x)\gg \frac{\ln x}{(\ln\ln x)^2} \] for all $x\geq 3$. The proof relies on properties of random subsets of the prime numbers.

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Alexander Kalmynin, Sergei Konyagin. 2023-03-26. Large gaps between sums of two squareful numbers. https://arxiv.org/abs/2303.14833

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