query: The highest power of $(n^r-1)!$
positive_passages.docid: 142347
positive_passages.text: What is the highest power of $n$ in $(n^r-1)!$
negative_passages.docid: 145519
negative_passages.text: Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
negative_passages.docid: 98448
negative_passages.text: Find the radius of convergence of $\sum_{n=1}^{\infty}{n!x^{n!}}$
negative_passages.docid: 102738
negative_passages.text: Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
negative_passages.docid: 4435
negative_passages.text: What does $\!\bmod(n,x^r-1)$ mean? [in AKS primality test]
negative_passages.docid: 62177
negative_passages.text: Prove that: $2^n < n!$ Using Induction
negative_passages.docid: 153763
negative_passages.text: Prove that $a_1!\cdots a_k! < n!$ whenever $a_1+\cdots+a_k < n$
negative_passages.docid: 154933
negative_passages.text: Prove $(p-k)!(k-1)!\equiv (-1)^k \text{ mod p }$
negative_passages.docid: 55557
negative_passages.text: Proof of Laplace transform of real number powers: $\mathcal{L} \{ t^n \} = \frac{n!}{s^{n + 1}}$
negative_passages.docid: 9997
negative_passages.text: For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
negative_passages.docid: 120554
negative_passages.text: highest power of prime $p$ dividing $\binom{m+n}{n}$
negative_passages.docid: 1409
negative_passages.text: Proving that the given set has at most $2^{n-1}$ elements
negative_passages.docid: 102717
negative_passages.text: Real analysis of powers
negative_passages.docid: 44701
negative_passages.text: How to find maximum $x$ that $k^x$ divides $n!$
negative_passages.docid: 100558
negative_passages.text: Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
negative_passages.docid: 118105
negative_passages.text: What is the radius of convergence of $\sum z^{n!}$?
negative_passages.docid: 133528
negative_passages.text: $\lvert K(\alpha_1,\dots,\alpha_n) : K \rvert$ is a divisor of $n!$