On the solutions of the congruence 𝑛²≡1(𝑚𝑜𝑑𝜙²(𝑛))

On the solutions of the congruence $n^{2}\equiv 1~(mod~\phi ^{2}(n))$
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by Florian Luca and Michal Křǐžek PDF

Proc. Amer. Math. Soc. 129 (2001), 2191-2196 Request permission

In this note, we show that if $n$ is a positive integer satisfying the congruence $n^{2}\equiv 1~ (mod~\phi ^{2}(n))$, then $n\le 3$.

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