query: $\sum_{n=1}^{p-1}{\frac{1}{n}} = \frac{A_p}{B_p}$ What is $A_p$ (mod $p^2$) where $\frac{A_p}{B_p}$ is a reduced form fraction?
positive_passages.docid: 20407
positive_passages.text: Proof of Wolstenholme's theorem
negative_passages.docid: 99003
negative_passages.text: How do we calculate this sum $\sum_{n=1}^{\infty} \frac{1}{n(n+1)\cdots(n+p)}$?
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: 21846
negative_passages.text: Let p be a prime. Consider the equation $\frac1x+\frac1y=\frac1p$. What are the solutions?
negative_passages.docid: 110752
negative_passages.text: $g^\frac{p-1}{2} \equiv -1 \ (mod \ p)$
negative_passages.docid: 74898
negative_passages.text: $1^n +2^n + \cdots +(p-1)^n \mod p =$?
negative_passages.docid: 54473
negative_passages.text: Value of $\sum 1/p^p$
negative_passages.docid: 52987
negative_passages.text: $\sum_{n=-\infty}^{\infty}\frac{1}{(n+\alpha)^2}=\frac{\pi^2}{(\sin \pi \alpha)^2}$?
negative_passages.docid: 83753
negative_passages.text: Why $\,p \cdot (p^{-1} \mod q) + q \cdot (q^{-1} \mod p) = pq + 1$?
negative_passages.docid: 153226
negative_passages.text: Proof of $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
negative_passages.docid: 101057
negative_passages.text: Show that $1^{p-1} + 2^{p-1} +\ldots + (p-1)^{p-1} \equiv -1 \mod p$
negative_passages.docid: 27287
negative_passages.text: $-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$
negative_passages.docid: 50972
negative_passages.text: Prove that $\sum_{x=1}^{n} \frac{1}{x (x+1)(x+2)} = \frac{1}{4} - \frac{1}{2 (n+1) (n+2)}$
negative_passages.docid: 114346
negative_passages.text: Why is $a^{-1}$ mod $p$ equal to $a^{p-2}$ mod $p$?
negative_passages.docid: 18714
negative_passages.text: $\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$
negative_passages.docid: 158616
negative_passages.text: A closed form for the sum $S = \frac {2}{3+1} + \frac {2^2}{3^2+1} + \cdots + \frac {2^{n+1}}{3^{2^n}+1}$ is ...
negative_passages.docid: 57503
negative_passages.text: How find $\sum_{k \in A} \frac{1}{k-1} $ for $ A = \{ m^n| \text{ } m, n \in Z \text { and } m, n \ge 2 \} $