Determine all positive integer n for which $2^{n} + 1$ is divisible by 3.

Open in App

Solution

$2^{n} + 1$ is divisible by 3.
$\Rightarrow (3 - 1)^{n} + 1$ is divisible by 3
$\Rightarrow (- 1)^{n} + 1$ is divisible by 3
$\Rightarrow n i s o d d$
Set of all odd natural numbers in the set of all those positive integer for which $2^{n} + 1$ is divisible by 3.

Suggest Corrections

Similar questions

n

2^{n} + 1

3.

3^{2 n} - 2 n + 1

f (n) = n! + (n + 1)! + (n + 2)!

49

50^{n} - 49 n - 1

49^{3}

n

{(\sqrt{3} + 1)}^{2 n}

2^{n + 1}

n ϵ N .

Join BYJU'S Learning Program