Prove (or disprove) that $3^{2n+3}+40n-27$ is divisible by $64$ for any $n$ integer
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
8364
To show that Fermat number $F_{5}$ is divisible by $641$.
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
17965
Prove 24 divides $u^3-u$ for all odd natural numbers $u$
55060
Prove that $n^2+n+41$ is prime for $n<40$
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
113119
Use the division algorithm to prove that 3|(n³ + 2n) for all n ∈ ℕ
16407
$24\mid n(n^{2}-1)(3n+2)$ for all $n$ natural problems in the statement.
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$