query: What is the product of $p_i-1 \over p_i$
positive_passages.docid: 147864
positive_passages.text: Convergence of infinite product of prime reciprocals?
negative_passages.docid: 14403
negative_passages.text: If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
negative_passages.docid: 147611
negative_passages.text: Given $P$ idempotent, show that $I-P$ is idempotent.
negative_passages.docid: 134709
negative_passages.text: Express symmetric polynomial $\prod_{i < j} (X_i+X_j)$ in terms of elementary symmetric functions
negative_passages.docid: 90921
negative_passages.text: Product of two primitive polynomials
negative_passages.docid: 46431
negative_passages.text: Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
negative_passages.docid: 81124
negative_passages.text: Infinite product problem: $\sum p_n0$
negative_passages.docid: 144148
negative_passages.text: Find the value of $P(1)$
negative_passages.docid: 27449
negative_passages.text: Product of Divisors of some $n$ proof
negative_passages.docid: 3475
negative_passages.text: Hadamard Product of $e^z-1$
negative_passages.docid: 14815
negative_passages.text: How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
negative_passages.docid: 151520
negative_passages.text: About the parity of the product $(a_1-1)(a_2-2)\cdots(a_n-n)$
negative_passages.docid: 83407
negative_passages.text: How to show that that $q \mid p-1$?
negative_passages.docid: 51465
negative_passages.text: New, elegant proofs for $\varphi(p^{k})=p^{k}-p^{k-1}$
negative_passages.docid: 84437
negative_passages.text: Prove that the projection $p_i$ from the product space $X_I S_i \tau$ into $S_i \tau_i$ is open for each $i \in I$
negative_passages.docid: 26658
negative_passages.text: A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$