query: For prime $p\equiv 1(\operatorname{mod} 4)$ , can $\dfrac {p^p-1}{p-1}$ be a prime?
positive_passages.docid: 20980
positive_passages.text: Prove that $\frac{p^p-1}{p-1}$ is not prime if $p \equiv 1 \pmod 4$
negative_passages.docid: 38727
negative_passages.text: Modular Exponentiation and Primes
negative_passages.docid: 141418
negative_passages.text: When is $\mathbb{F}_p[x]/(x^2-2)\simeq\mathbb{F}_p[x]/(x^2-3)$ for small primes?
negative_passages.docid: 68221
negative_passages.text: Question regardles primes and the fundamental theorem of arithmetic
negative_passages.docid: 68635
negative_passages.text: When is $2$ a quadratic residue mod $p$?
negative_passages.docid: 147101
negative_passages.text: Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
negative_passages.docid: 32618
negative_passages.text: Suppose $p$ is a prime number such that $(p-1)/4$ and $(p+1)/2$ are also primes. Show that $p=13$
negative_passages.docid: 145752
negative_passages.text: Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
negative_passages.docid: 153862
negative_passages.text: A question about a primitive root mod $p=2^{2^k}+1$, where $p$ is prime.
negative_passages.docid: 126725
negative_passages.text: If $p$ is prime and $p$ $\equiv$ $1$ (mod 4), then the congruence $x^2$ $\equiv$ $-1$ (mod $p$) has two incongruent solutions...
negative_passages.docid: 94017
negative_passages.text: If p is a prime and a ∈Z. How do we prove that the congruence x^x ≡ a (mod p) is solvable?
negative_passages.docid: 114346
negative_passages.text: Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
negative_passages.docid: 78343
negative_passages.text: $4x^2+1$ factors only into $4y+1$ primes
negative_passages.docid: 60305
negative_passages.text: Proving the congruence $p^{q-1}+q^{p-1} \equiv 1 \pmod{pq}$
negative_passages.docid: 75528
negative_passages.text: $x^2-x+1$ has a root $\!\bmod p\,$ for infinitely many primes $p$
negative_passages.docid: 148647
negative_passages.text: If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
negative_passages.docid: 23153
negative_passages.text: $\bmod p\!:\ x^2\equiv 1\iff x\equiv \pm1\ $ for prime $p$