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
Abstract:
In this note, we show that if $n$ is a positive integer satisfying the congruence $n^{2}\equiv 1~ (mod~\phi ^{2}(n))$, then $n\le 3$.References
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Additional Information
- Florian Luca
- Affiliation: Mathematical Institute, Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
- Address at time of publication: Instituto de Matemáticas de la UNAM, Campus Morelia, Apartado Postal 61-3 (Xangari), CP. 58 089, Morelia, Michoácan, Mexico
- MR Author ID: 630217
- Email: luca@math.cas.cz, fluca@matmor.unam.mx
- Michal Křǐžek
- Affiliation: Mathematical Institute, Academy of Sciences, Žitná 25, 115 67 Praha 1, Czech Republic
- Email: krizek@math.cas.cz
- Received by editor(s): November 16, 1999
- Published electronically: January 17, 2001
- Communicated by: David E. Rohrlich
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2191-2196
- MSC (2000): Primary 11A07, 11A25, 11D09
- DOI: https://doi.org/10.1090/S0002-9939-01-05929-9
- MathSciNet review: 1823899