If 3 divides $n$, then 3 divides the product $n$($n$+1)($n$+2). Why is this?
62556
Prove $3|n(n+1)(n+2)$ by induction
5841
Proving prime $p$ divides $\binom{p}{k}$ for $k\in\{1,\ldots,p-1\}$
102757
Prove that either $m$ divides $n$ or $n$ divides $m$ given that $\operatorname{lcm}(m,n) + \operatorname{gcd}(m,n) = m + n$?
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
55437
When does $2^{n}$ divide $3^{n}-1$
141404
Infinite product: $\prod_{k=2}^{n}\frac{k^3-1}{k^3+1}$
106562
Is $3 \ge 1$ or is it just $3 > 1$?
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
23427
How to prove there are no more positive integers that are products of 2 and 3 consecutive numbers?
9319
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
37596
If $\gcd(a,b)= 1$ and $a$ divides $bc$ then $a$ divides $c\ $ [Euclid's Lemma]
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
56566
If ${n \choose 3} + {n+3-1 \choose 3} = (n)_3$, compute $n$.
125855
Prove: The product of any three consecutive integers is divisible by $6$.
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
38719
In this case, why must $p$ divide $|G/N|$?