Prove that $5 \mid 3^{3n+1}+2^{n+1}$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
89175
Proof of $(a+b)^{n+1}$
62556
Prove $3|n(n+1)(n+2)$ by induction
81136
Prove by induction that... $1+3+5+7+...+(2n+1)=(n+1)^2$ for every $n \in \mathbb N$
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
114867
Prove $\forall n\geq 2,n\in\mathbb{Z}$, $(n+1)\mid(n^3+1)$
6488
Proof that $n^3 + 3n^2 + 2n$ is a multiple of $3$.
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
125297
Induction to prove $2n + 3 < 2^n$
146093
Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?