How can I prove that $4^n-1$ is divisible by 3?
39175
Prove by induction that $\forall n \in\mathbb N$, $3\mid4^{n}-1$.
143772
How can I algebraically prove that $2^n - 1$ is not always prime?
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
50534
Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
46158
A positive integer is divisible by $3$ iff 3 divides the sum of its digits
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
124816
Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
82358
How to prove that $4^m + 5^m$ is divisible by 9 when m is an odd number
62100
Show that $n^3-n$ is divisible by $6$ using induction
27428
Divisibility test for $4$
20477
Prove that $\gcd(3^n-2,2^n-3)=\gcd(5,2^n-3)$
55437
When does $2^{n}$ divide $3^{n}-1$
31074
Mathematical Induction divisibility $8\mid 3^{2n}-1$
150528
Pythagorean triples $(a,b,c)$ and divisibility of $a$ or $b$ by $3$.