Prove: The product of any three consecutive integers is divisible by $6$.
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
26857
In any Pythagorean triplet at least one of them is divisible by $2$, $3$ and $5$.
63240
Every two consecutive integers are coprime.
80365
Prove that $n$ is divisible by $6$
63300
Product of Consecutive Integers is Not a Power
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
155926
Prove there are k consecutive non-squarefree integers
105405
Product of three consecutive positive integers is never a perfect power
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
96169
$n$ divides a product of $n$ consecutive integers (by $n$ divides one of them)
10744
Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
113359
Proving that $x^2 + 4$ is not divisible by $3$
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
54699
Product of pairwise coprime integers divides $b$ if each integer divides $b$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$