Question

Let $P(n):n^2-n+41$ is a prime number$"$, then

• A. $P(1)$ is not true
• B. $P(3)$ is not true
• C. $P(5)$ is not true
• D. $P(41)$ is not true

Answer 1

Answer: (D)

$P\left(1\right)$ is ''$1^2-1+41$ is prime'' i.e. $41$ is prime,
which is true. Similarly, $P\left(3\right)$ and $P\left(5\right)$ are also true.
Now $P\left(41\right)$ is ${}^{\prime \prime }41^2-41+41$ is prime''
i.e. $41^2$ is prime, which is certainly false.