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On the equation $\varphi (n)=\varphi (n+1)$

Volume 196 / 2020

Paul Kinlaw, Mitsuo Kobayashi, Carl Pomerance 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 $8$.

Authors

  • Paul KinlawHusson University
    1 College Circle
    Bangor, ME 04401, U.S.A.
    e-mail
  • Mitsuo KobayashiMathematics Department
    Dartmouth College
    Hanover, NH 03755, U.S.A.
    e-mail
  • Carl PomeranceMathematics Department
    Dartmouth College
    Hanover, NH 03755, U.S.A.
    e-mail

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