Prove that $n\left(n(n-3)+8\right)$ is divisible by 3
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
80365
Prove that $n$ is divisible by $6$
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
48655
Find all n such that : $3 \mid (n2^{n}+1)$
146665
Prove that $f(x)=8$ for all natural numbers $x\ge{8}$
62556
Prove $3|n(n+1)(n+2)$ by induction
77383
Prove that $n^3=n \text{ mod }6$ for every integer $n$.
91921
Divisibility of $n\cdot2^n+1$ by 3.
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
21612
How to prove this form of $n$?
85941
Proof by induction that $n^3 - n$ is divisible by $6$
35666
How to prove the divisibility rule for $3\, $ [casting out threes]
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
41563
Prove that if the sum of digits of a number is divisible by 3, so is the number itself.
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
139718
Prove $6 \nmid [\left( \sqrt[3]{28} - 3 \right)^{-n}]$
27784
Proving that $\left(\mathbb Q[\sqrt p_1,\dots,\sqrt p_n]:\mathbb Q\right)=2^n$ for distinct primes $p_i$.