Show that $C(n,k) = C(n-1,k) + C(n-1,k-1)$
424
Proving Pascal's Rule : ${{n} \choose {r}}={{n-1} \choose {r-1}}+{{n-1} \choose r}$ when $1\leq r\leq n$
85688
How to show $\gcd(ac, bd) = \gcd(a,d) * \gcd(b,c)$
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
109745
If $(a,k)=(b,m)=1$, prove that $(ab,km)=(a,m)(b,k)$.
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
5149
Show $\binom{a}{b}\binom{b}{c}=\binom{a}{a-c}\binom{a-c}{a-b}$
70282
Help finding a combinatorial proof of $k {n \choose k } = n {n - 1 \choose k -1}$
89552
proving combinatorics identity - $\sum_{k=0}^m{n-k \choose m-k}={n+1 \choose m}$
37569
Prove that $\binom{n}{r} + \binom{n}{r+1} = \binom{n+1}{r+1} $
69943
why is ${n+1\choose k} = {n\choose k} + {n\choose k-1}$?
24845
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
121279
Proving an Combination formula $ \binom{n}{k} = \binom{n-1}{k}+\binom{n-1}{k-1}$
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
111951
Prove $\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n-k}{m-k}$
72026
Induction proof of $\sum_{k=1}^{n} \binom n k = 2^n -1 $
55266
Prove that $(n+1)^{n-1}<n^n$
133181
Hint on how to prove the identity $\sum_{0 \leq k \leq n } \binom{k}{m} = \binom{n + 1}{m + 1}$