$k$ divides the product of $k$ consecutive integers (case $k=2,3)$
40692
Proving by strong induction that $\forall n \ge 2, \;\forall d \ge 2 : d \mid n(n+1)(n+2)...(n+d-1) $
102154
If $a$ and $b$ are consecutive integers, prove that $a^2 + b^2 + a^2b^2$ is a perfect square.
123626
Prove that even $n$ can be partitioned to $\frac n2$ edges
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
142534
Proof of $k {n\choose k} = n {n-1 \choose k-1}$ using direct proof
11470
Divisibility of integers
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
114796
Direct proof that the product of odd integers is odd
78593
Prove that the product of four consecutive positive integers plus one is a perfect square
131476
consecutive prime power
126574
Proving $\prod_k \sin \pi k / n = n / 2^{n-1}$
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
108563
Detecting consecutive integers in a list
47960
Given any $10$ consecutive positive integers , does there exist one integer which is relatively prime to the product of the rest ?
117761
When is $\binom{n}{k}$ divisible by $n$?
94516
If $3$ divides $a^2 + b^2$, then $3$ divides $a$ and $3$ divides $b$
136964
Prove there exist 135 consecutive integers that each have a perfect cube $>1$ that divides it.