Prove that $5\mid 8^n - 3^n$ for $n \ge 1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
67527
Proof by Induction that $3^n ≥ 1+2^n$
1258
Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
75329
Use induction to prove that $F_n \ge \sqrt 2 ^n$ for $n \ge 6$
11867
Prove by induction that $n < 2^n$ for all $n \ge 1$
280
Prove by induction that $5^n - 1$ is divisible by $4$.
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
127293
Prove that $(a-b) \mid (a^n-b^n)$
55266
Prove that $(n+1)^{n-1}<n^n$
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
27147
Proving $n! > n^3$ for all $n > a$
143543
Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
141088
Proof : $2^{n-1}\mid n!$ if and only if $n$ is a power of $2$.
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?