On equations $σ(n)=σ(n+k)$ and $\varphi(n)=\varphi(n+k)$

Details On equations $σ(n)=σ(n+k)$ and $\varphi(n)=\varphi(n+k)$ On equations $σ(n)=σ(n+k)$ and $\varphi(n)=\varphi(n+k)$

2010-01-14

arxiv.org/abs/1001.2511v1

Mathematics

Number Theory

9 pages, sent to J. Combinatorics and Number Theory

Scientific paper

We study the distribution of solutions of equations $\sigma(n)=\sigma(n+k)$
and $\varphi(n)=\varphi(n+k)$. We give new upper bounds for these solutions.

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