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 $''41^{2} -41+41$ is prime''
i.e. $41^{2}$ is prime, which is certainly false.