query: Show that: $-1 \equiv (-1)^{(p-1)/2}x^2 \pmod p$
positive_passages.docid: 7932
positive_passages.text: $(p\!-\!1\!-\!h)!\,h! \equiv (-1)^{h+1}\!\!\pmod{\! p}\,$ [Wilson Reflection Formula]
negative_passages.docid: 74512
negative_passages.text: How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?
negative_passages.docid: 2218
negative_passages.text: Prove that $(n-1)! \equiv -1 \pmod{n}$ iff $n$ is prime [Wilson's Theorem]
negative_passages.docid: 44729
negative_passages.text: Prove $g$ is a generator if $g^q=1 \pmod p$
negative_passages.docid: 85287
negative_passages.text: Prove that, for $p > 3$, $(\frac 3p) = 1$ when $p \equiv 1,11 \pmod{12}$ and $(\frac 3p) = -1$ when $p \equiv 5,7 \pmod{12}$
negative_passages.docid: 4970
negative_passages.text: For $n \geq 2$, show that $n \nmid 2^{n}-1$
negative_passages.docid: 135465
negative_passages.text: Group theory proof of existence of a solution to $x^2\equiv -1\pmod p$ iff $p\equiv 1 \pmod 4$
negative_passages.docid: 45171
negative_passages.text: How prove this $(p-1)!\left(1+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{p-1}\right)\equiv 0\pmod{p^2}$
negative_passages.docid: 30630
negative_passages.text: Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$
negative_passages.docid: 62382
negative_passages.text: I suppose $(a,m)=(a-1,m)=1$, show that $1+a+a^2+\ldots+a^{\phi(m)-1}\equiv0\pmod m$
negative_passages.docid: 122741
negative_passages.text: $x^2$ is congruent to $-1 \bmod p$
negative_passages.docid: 38876
negative_passages.text: $r! \equiv (−1)^k \pmod p$
negative_passages.docid: 132984
negative_passages.text: $\sum\limits_{k=0}^{\frac{p-1}2}3^k\binom{p}{k}\equiv 2^p-1\pmod{p^2}$
negative_passages.docid: 144017
negative_passages.text: How to find the smallest $n$ such that $n^a\equiv 1 \pmod p$
negative_passages.docid: 77076
negative_passages.text: Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
negative_passages.docid: 89590
negative_passages.text: The number of solutions of $ax^2+by^2\equiv 1\pmod{p}$ is $ p-\left(\frac{-ab}{p}\right)$
negative_passages.docid: 132587
negative_passages.text: Prove that the product of coprimes must be congruent to $-1$ or $1 \pmod{m}$