Prove that $6^n+8^n$ is divisible by $7$ iff $n$ is odd
8366
Proof of $a^n+b^n$ divisible by $a+b$ when $n$ is odd
78416
Show that $7$ divides $a^{15}-a^3$ for any integer $a$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
17194
$6^{(n+2)} + 7^{(2n+1)}$ is divisible by $43$ for $n \ge 1$
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
125040
Show by induction : $n^7-n$ is a multiple of 7
62100
Show that $n^3-n$ is divisible by $6$ using induction
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
110256
Let $a,b \in {\mathbb{Z_+}}$ such that $a|b^2, b^3|a^4, a^5|b^6, b^7|a^8 \cdots$, Prove $a=b$
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
17047
Prove that if n is even then $n^2$ is even and if n is odd then $n^2$ is odd?
31708
Divisibility criteria for $7,11,13,17,19$
17660
Show that the odd prime divisors of $n^2+n+1$ are of form $6k+1$ (exclude 3)
129238
Divisibility of $2^n - 1$ by $2^{m+n} - 3^m$.