What is the maximum value of $n$ for which $3^n$ divides 1000!?
44701
How to find maximum $x$ that $k^x$ divides $n!$
134348
When is $(p - 1)! + 1$ a power of $p$?
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
106380
What is $n!$ when $n=0$?
120554
highest power of prime $p$ dividing $\binom{m+n}{n}$
72406
Last two digits of $2^{1000}$ via Chinese Remainder Theorem?
29578
Why is $\binom{2n}{n} \asymp \Theta \big(\frac{2^{2n}}{\sqrt{n}}\big)$?
148567
Given $a,b$, what is the maximum number which can not be formed using $na + mb$?
8609
Prove by induction that $n!>2^n$
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
29325
Maximum Proof (Average?)
114404
For which positive integer values of $n$ does $a|mn-b?$
1895
How to show that $2730\mid n^{13}-n\;\;\forall n\in\mathbb{N}$
147849
Does $(n!)/n^{1000}$ diverge or converge
62392
Find the value of- $\lim_{x \rightarrow -\infty}\sum_{k=1}^{1000} \frac{x^k}{k!}$
144512
Find the greatest value of $a^2\cdot b^3$ where $a+b=10$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$