Prove that $2x^3+3x^2+x$ is always divisible by 6 if x is an integer.
128306
Show that for all $n ∈ Z$, $2n^3 + 3n^2 + n$ is divisible by both 2 and 3.
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
139230
Prove that for every positive integer, this polynomial is divisible by 24.
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
124816
Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
108746
Prove that there exist two integers such that i - j is divisible by n.
106981
Prove that $(a+1)(a+2)...(a+b)$ is divisible by $b!$
118918
Understanding a proof that $2x + 3y$ is divisible by $17$ iff $9x + 5y$ is divisible by $17$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
85941
Proof by induction that $n^3 - n$ is divisible by $6$
91044
Why is a number that is divisible by $2$ and $3$, also divisible by $6$?
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$