Question

Which of the following number(s) is/are not prime?
$\left(1\right)2^{2011}+1\left(2\right)2^{2012}-1\left(3\right)2^{2013}+1$

• A. 1 and 2
• B. 1 and 3
• C. 2 and 3
• D. 1, 2 and 3

Answer 1

The correct option is D

1, 2 and 3

$\frac{a^n+b^n}{a+b}\Rightarrow$ Remainder = 0, if n is odd.
$2^{2011}+1$ and $2^{2013}+1$ are divisible by 3.
Now, $2^{2012}-1$ can be written as $4^{1006}-1$.
$4^{1006}-1$ = $(-1{)}^{1006}-1$ is divisible by 5.

Hence, none of the given numbers is a prime number.