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- W4287863586 abstract "We show that for some $kle 3570$ and all $k$ with $442720643463713815200|k$, the equation $phi(n)=phi(n+k)$ has infinitely many solutions $n$, where $phi$ is Euler's totient function. We also show that for a positive proportion of all $k$, the equation $sigma(n)=sigma(n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao and PolyMath." @default.
- W4287863586 created "2022-07-26" @default.
- W4287863586 creator A5090468558 @default.
- W4287863586 date "2020-02-27" @default.
- W4287863586 modified "2023-09-25" @default.
- W4287863586 title "Solutions of $phi(n)=phi(n+k)$ and $sigma(n)=sigma(n+k)$" @default.
- W4287863586 doi "https://doi.org/10.48550/arxiv.2002.12155" @default.
- W4287863586 hasPublicationYear "2020" @default.
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