Proof that $N/1*(N-2)/2*(N-3)/3...$ is always integral? (Algorithm for Combinations)
30136
Proof that a Combination is an integer
11612
How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$?
56566
If ${n \choose 3} + {n+3-1 \choose 3} = (n)_3$, compute $n$.
157601
Proof a formula of the Fibonacci sequence with induction
118372
Combination proof for $n(n+1)2^{n-2}=\sum_{k=1}^{n}k^2\binom{n}{k}$
56624
Prove that $0!+1! + 2! + 3! + ..... + n!$ $\neq$ $p^\text{r}$, where $n \geqslant 3$ and $n$, $p$ and $r$ are three integers
15100
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
10917
Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $
82913
Is this a proof of Fermat's Last Theorem where n = 3?
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
57746
Prove that, for any set of consecutive integers with an odd number of terms, the sum of the integers is always a multiple of the number of terms.
4201
Prove $\sum\binom{n}{k}2^k = 3^n$ using the binomial theorem
118018
Show $ (n+1)^{1/3}-n^{1/3}=O\left(n^{-2/3}\right) $
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
63510
Prove: $\binom{n}{k}^{-1}=(n+1)\int_{0}^{1}x^{k}(1-x)^{n-k}dx$ for $0 \leq k \leq n$
62556
Prove $3|n(n+1)(n+2)$ by induction
110441
Closed form for a formula with a summation over $i\binom{n-i}{k-1}$, and combinatorial proof?