Proof if $n$ is divisible by $3$ then the sum of the digits of $n$ are a multiple of $3$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
42526
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
80365
Prove that $n$ is divisible by $6$
116356
Combinatorial proof of $2 \cdot 3^0 + 2 \cdot 3^1 + 2 \cdot 3^2 + \cdots 2 \cdot 3^{n-1} = 3^n-1$
125210
proof: primitive pythagorean triple, a or b has to be divisible by 3
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
106847
Proof that $n^3+2n$ is divisible by $3$
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
125855
Prove: The product of any three consecutive integers is divisible by $6$.
45460
Proof verification of a number theory problem involving sequences.
126124
Why is the sum of the digits in a multiple of 9 also a multiple of 9?
135892
Understanding the proof for showing that there are infinitely many $n\in\mathbb{Z}^+$ such that $n!+1$ is divisible by at least two distinct primes
150430
Let $S={1, 2, 3, 4, ....., 2070}$ find the number of subsets of $S$ whose sum of elements in $S$ is divisible by 9
1507
The product of $n$ consecutive integers is divisible by $n$ factorial
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$