The product of any three consecutive natural numbers is divisible by 6
125855
Prove: The product of any three consecutive integers is divisible by $6$.
22977
How many $6$-integer subsets of $\{1, 2, 3, \ldots, 20\}$ have no consecutive integers?
61340
Prove that there exists bipartite graph with this degree sequence: $(3,3,3,3,3,5,6,6,6,6,6,6,6,6)$
60615
Product of $5$ consecutive integers cannot be perfect square
124890
Divisibility within a block of natural numbers
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
48850
Consecutive composite numbers
116970
On the number divisors of a number
63240
Every two consecutive integers are coprime.
62100
Show that $n^3-n$ is divisible by $6$ using induction
82071
divisor of a product of integers is a product of divisors
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
47799
Show that the number or $r$ combinations of $X$ which contain no consecutive integers is given by $\binom{n-r+1}{r}$
142956
Prove that for any positive integer n there is a sequence of n consecutive composite numbers.
113980
Prove that a set of nine consecutive integers cannot be partitioned into two subsets with same product