Show that $7\mid(3^{2n+1}+2^{n+2})$ for all $n\in\mathbb{N}$
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$
95000
Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$
22093
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
138846
Prove by induction that $3\mid n^4-n^2$ for all $n \in \mathbb{Z^+}$, $n\ge2$.
119118
Prove $n\mid \phi(2^n-1)$
35945
Proof that if $\gcd(a,b) = 1$ and $a\mid n$ and $b\mid n$, $ab \mid n$
141105
Show that there exists a $3 × 3$ invertible matrix $M$ with entries in $\mathbb{Z}/2\mathbb{Z}$ such that $M^7 = I_3$.
72639
Show that $\sum_{k=0}^n\binom{3n}{3k}=\frac{8^n+2(-1)^n}{3}$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
145041
Given that $p$ is a prime and $p\mid a^n$, prove that $p^n\mid a^n$.
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
99428
Prove that $3^{2n-1} + 2^{n+1}$ is always a multiple of $7$.
126888
How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
50894
Prove that $6$ divides $n(n + 1)(n + 2)$
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd