query: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
positive_passages.docid: 155743
positive_passages.text: Why does the equation $x^2\equiv2 \pmod 5$ have no solutions?
negative_passages.docid: 157652
negative_passages.text: Fermat's Last Theorem for Gaussian Integers (excluding the integers or  same pure imaginaries)
negative_passages.docid: 32136
negative_passages.text: How to prove Lucas's Converse of Fermat's Little Theorem without using primitive root?
negative_passages.docid: 82913
negative_passages.text: Is this a proof of Fermat's Last Theorem where n = 3?
negative_passages.docid: 157213
negative_passages.text: Application of Luca's theorem
negative_passages.docid: 83542
negative_passages.text: A natural problem in $\textrm{S}_2^\textrm{P}$?
negative_passages.docid: 13656
negative_passages.text: Prove existence of a real root.
negative_passages.docid: 49938
negative_passages.text: Proof of $a^{\phi (n) +1} \equiv a \pmod{\! n} $ Carmichael generalization of Fermat-Euler's theorem.
negative_passages.docid: 115299
negative_passages.text: Elements of $\mathbb{F}_p$ having cube roots in $\mathbb{F}_p$
negative_passages.docid: 136894
negative_passages.text: Reference request: Clean proof of Fermat's last theorem for $n=3$.
negative_passages.docid: 51153
negative_passages.text: Number of solutions to $x^2\equiv a\pmod m$
negative_passages.docid: 4435
negative_passages.text: What does $\!\bmod(n,x^r-1)$ mean? [in AKS primality test]
negative_passages.docid: 20908
negative_passages.text: How to compute $k$'th roots $\!\bmod n$?
negative_passages.docid: 1425
negative_passages.text: The Chinese Remainder Theorem for Rings.
negative_passages.docid: 29231
negative_passages.text: Proof of : $x^{n}\equiv x^{\varphi(m)+[n \bmod \varphi(m)]} \mod m$
negative_passages.docid: 34323
negative_passages.text: Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
negative_passages.docid: 139659
negative_passages.text: Find all $n$ with $\!\bmod n\!:\, a\,$ invertible $\Rightarrow a^{-1} \equiv a,\,$ i.e. $a^2\equiv 1$