To determine multiplicity of $2$ in $n!$
29693
Would someone please explain this argument? (Legendre formula)
49158
Multiplicity of eigenvalues
27141
Combinatorics identity question
102721
Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
77128
Necessary and Sufficient conditions for $(i \, j)$ and $(1 \, 2 \, \dotsc \, n)$ generate $S_n$.
15000
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
71245
$2 \times 2 $ Orthogonal Group
150156
Proving that $S_n$ has order $n!$
22962
How to show $\binom{2p}{p} \equiv 2\pmod p$?
87320
Proving identities like $\sum_{k=1}^nk{n\choose k}^2=n{2n-1\choose n}$ combinatorially
103504
Weird $3^n$ in an identity to be combinatorially proved
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
155372
Find the number of permutations in $S_n$ containing fixed elements in one cycle
21000
Calculating $\sum_{k=1}^nk(k!)$ combinatorially
26087
Find all natural numbers $n > 1$ and $m > 1$ such that $1!3!5!\cdots(2n - 1)! = m!$
43058
If $n > 2$, prove that the order of the multiplicative group of units modulo n, $U_n$, is even.
24588
Proving the combinatorial identity ${n \choose k} = {n-2\choose k-2} + 2{n-2\choose k-1} + {n-2\choose k}$