On the solutions of the congruence \(n^{2}\equiv 1\pmod {\varphi^{2}(n)}\) (Q2718988)
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scientific article; zbMATH DE number 1597880
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the solutions of the congruence \(n^{2}\equiv 1\pmod {\varphi^{2}(n)}\) |
scientific article; zbMATH DE number 1597880 |
Statements
14 May 2001
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congruences
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Euler's phi-function
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On the solutions of the congruence \(n^{2}\equiv 1\pmod {\varphi^{2}(n)}\) (English)
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The authors prove that the solutions \(n\) of the congruence \(n^2\equiv 1 \pmod {\varphi^2(n)}\) satisfy \(n\leq 3\). The proof is nontrivial and uses in particular upper bounds for the minimal solutions of Pell-Fermat equations.
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