Prove that if $3\mid n^2 $ then $3\mid n $.
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
62556
Prove $3|n(n+1)(n+2)$ by induction
4141
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
6165
Proof by Induction $n^2+n$ is even
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
135614
Show that $2^n > n^2$ whenever n>4.
52930
Prove or disprove : $a^3\mid b^2 \Rightarrow a\mid b$
56878
Proof that $a\mid b \land b\mid c \Rightarrow a\mid c $