Prove that $(m,n)(n,k)(k,n)[m,n,k]^2=[m,n][n,k][k,n](m,n,k)^2$
65503
Identity involving LCM and GCD: $\frac{[a,b,c]^2}{[a,b][b,c][c,a]}=\frac{(a,b,c)^2}{(a,b)(b,c)(c,a)}$
120074
Prove by Combinatorial Argument that $\binom{n}{k}= \frac{n}{k} \binom{n-1}{k-1}$
154703
Use combinatorics to prove $L\left(n,k\right)=\sum_{j=0}^{n}{ n\brack j}{j\brace k}$
63879
Prove that $\sum_{k=0}^r {m \choose k} {n \choose r-k} = {m+n \choose r}$
9522
Proving $k \binom{n}{k} = n \binom{n-1}{k-1}$
25961
Prove: $\binom{n}{0}F_0+\binom{n}{1}F_1+\binom{n}{2}F_2+\cdots+\binom{n}{n}F_n=F_{2n}$
49294
prove that $\operatorname{lcm}(n,m) = nm/\gcd(n,m)$
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
106008
Combinatorial Identity $(n-r) \binom{n+r-1}{r} \binom{n}{r} = n \binom{n+r-1}{2r} \binom{2r}{r}$
47670
Algebraic proof of $\sum_{i=0}^k{{n \choose i}{m \choose {k-i}}}= {{m+n}\choose k}$
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
20964
Proof that $n^2 < 2^n$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
21612
How to prove this form of $n$?
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
59252
Show $\sum_{k=0}^{m} \binom{n-k}{m-k}=\binom{n+1}{m}$