Geodesic
Large Gaps between Sums of Two Squareful Numbers
Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 589-596 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $x\geqslant 3$. The proof relies on properties of random subsets of the prime numbers.
Keywords: squareful numbers, large gaps, values of quadratic forms. 
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A. B. Kalmynin; S. V. Konyagin. Large Gaps between Sums of Two Squareful Numbers. Matematičeskie zametki, Tome 115 (2024) no. 4, pp. 589-596. http://geodesic.mathdoc.fr/item/MZM_2024_115_4_a8/

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