Question

Consider the statement : ''$P\left(n\right):n^2-n+41$ is prime.'' Then which of the following is true?

• A. Both $P\left(3\right)$ and $P\left(5\right)$ are false.
• B. $P\left(3\right)$ is false but $P\left(5\right)$ is true.
• C. $P\left(5\right)$ is false but $P\left(3\right)$ is true.
• D. Both $P\left(3\right)$ and $P\left(5\right)$ are true.

Answer 1

The correct option is D Both $P\left(3\right)$ and $P\left(5\right)$ are true.

$P\left(n\right)=n^2-n+41$
$P\left(3\right)=3^2-3+41=47$
$\Rightarrow P\left(3\right)$ is a prime.
$P\left(5\right)=5^2-5+41=61$
$\Rightarrow P\left(5\right)$ is also prime.
Since, both $P\left(3\right)$ and $P\left(5\right)$ are prime.
Therefore, both $P\left(3\right)$ and $P\left(5\right)$ are true.