If  P(n) be the statement ‘n2 – n + 41 is a prime number’, then show that P(1), P(2) are true but P(41) is not true.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

P(n): n2 – n + 41 is a prime number.
P(1): 12 – 1 + 41 is a prime number i.e. P(1) = 41 is prime, which is true.
P(2): 22 – 2 + 41 is a prime number  i.e. P(2) = 43 is prime, which is true.
P(41): 412 – 41 + 41 is a prime number  i.e. P(41) = 412 is prime, which is not true.

Answered by  | 4th Jun, 2014, 03:23: PM