On the equation $\varphi (n)=\varphi (n+1)$
Volume 196 / 2020
Acta Arithmetica 196 (2020), 69-92
MSC: 11N25, 11Y99.
DOI: 10.4064/aa190627-20-1
Published online: 15 June 2020
Abstract
We consider solutions of the equation $\varphi (n)=\varphi (n+1)$, where $\varphi $ denotes Euler’s function. Improving on previous work, we show that the reciprocal sum over all such $n$ is less than $8$.
