Proof of divisibility of 6
91044
Why is a number that is divisible by $2$ and $3$, also divisible by $6$?
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
130027
Give a direct proof of the fact that $a^2-5a+6$ is even for any $a \in \mathbb Z$
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
11470
Divisibility of integers
27428
Divisibility test for $4$
124240
Inductive proof of $\,9 \mathrel| 4^n+6n-1\,$ for all $\,n\in\Bbb N$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
43033
Proof on Catalan numbers
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
3632
Basic number theory proofs
152084
Binomial-Theorem proof
51638
pigeonhole principle divisibility proof
31555
Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)
63416
Prove $(n^5-n)$ is divisible by 5 by induction.