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- W4309134308 abstract "In this note, we prove by using T. Estermann's and S. Dimitrov's arguments with an elementary inequality that there are infinitely many $n$ for which all of the numbers $n^2+1,n^2+2$ and $n^2+3$ are squarefree. We also improve the error term slightly in the case of two consecutive numbers of the same form, so that we are able to prove the following asymptotic formula. begin{align*} sum_{nle X}mu^2(n^2+1)mu^2(n^2+2)mu^2(n^2+3)simdfrac{7}{18}prod_{p>3}left(1-dfrac{3+left(frac{-1}{p}right)+left(frac{-2}{p}right)+left(frac{-3}{p}right)}{p^2}right)X. end{align*}" @default.
- W4309134308 created "2022-11-23" @default.
- W4309134308 creator A5069503372 @default.
- W4309134308 date "2022-11-14" @default.
- W4309134308 modified "2023-09-27" @default.
- W4309134308 title "Three consecutive near-square squarefree numbers" @default.
- W4309134308 doi "https://doi.org/10.48550/arxiv.2211.07237" @default.
- W4309134308 hasPublicationYear "2022" @default.
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