How can I prove that a number of the form $2^{2n}-1$ is divisible by 3?
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
80365
Prove that $n$ is divisible by $6$
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
41563
Prove that if the sum of digits of a number is divisible by 3, so is the number itself.
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
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 $24$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
55437
When does $2^{n}$ divide $3^{n}-1$
28957
Verifying that $2^{44}-1$ is divisible by $89$
38904
Prove that $(a + b + c)^{13}$ is divisible by $abc$ if $b|a^3$, $c|b^3$ and $a|c^3$.
62100
Show that $n^3-n$ is divisible by $6$ using induction
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$