Prove without induction that $3^{4n}-2^{4n}$ is divisible by $65$
2522
Why is $a^n - b^n$ divisible by $a-b$?
19701
Prove $5\mid2^{4n}-1$ by induction
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.
130488
Prove by induction that $3\mid n^3 - n$
148330
Induction Proof for $F_{2n} = F^2_{n+1} - F^2_{n-1}$
28957
Verifying that $2^{44}-1$ is divisible by $89$
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
57041
How would you prove that $2^{50} < 3^{33}$ without directly calculating the values
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
46556
How to prove $3^{\log_4n} = n^{\log_43}$?
101927
Induction: Prove that $4^{n+1}+5^{2 n - 1}$ is divisible by 21 for all $n \geq 1$.
39716
Prove that $8(5)^n + 6(3)^{2n} - 80n - 14$ is divisible by $512$ for all $n \in \mathbb{N}$ by induction.
77579
Proof by induction that $ 169 \mid 3^{3n+3}-26n-27$