Prove $n=m^3-3m^2+2m$, for any integer $m$, then $n$ is a multiple of $6$.
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
139082
If $a,b,c>0$ and $a^3+b^3=c^3$ then prove that $a^2+b^2-c^2>6(c-a)(c-b)$.
88124
$M,N\in \Bbb R ^{n\times n}$, show that $e^{(M+N)} = e^{M}e^N$ given $MN=NM$
106965
How to algebraically prove $\binom{n+m}{2} = nm + \binom{n}{2} + \binom{m}{2}$?
9435
Prove that $1^2+2^2+\cdots+n^2=\frac{n(n+1)(2n+1)}{6}$ for $n \in \mathbb{N}$.
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
110703
How Can I prove (a+b) mod m = (a mod m) + (b mod m)) mod m?
102334
How can you prove $\frac{n(n+1)(2n+1)}{6}+(n+1)^2= \frac{(n+1)(n+2)(2n+3)}{6}$ without much effort?
112541
Prove that $n^2 + 2^n$ is composite if $n\not\equiv3\pmod{6}$.
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
125297
Induction to prove $2n + 3 < 2^n$
90916
Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
80365
Prove that $n$ is divisible by $6$
109576
Prove that $\binom{m+n}{m}=\sum\limits_{i=0}^m \binom{m}{i}\binom{n}{i}$
136868
Prove that $\sqrt{a^2+3b^2}+\sqrt{b^2+3c^2}+\sqrt{c^2+3a^2}\geq6$ if $(a+b+c)^2(a^2+b^2+c^2)=27$
136894
Reference request: Clean proof of Fermat's last theorem for $n=3$.