Consider the statement : "P(n) : \(n^2 - n + 41\) is prime". Then which one of the following is true ?
Show Hint
- P(5) is false but P(3) is true
- Both P(3) and P(5) are true
- P(3) is false but P(5) is true
- Both P(3) and P(5) are false
The Correct Option is B
Solution and Explanation
\(P(5) = 25 - 5 + 41 = 61\). 61 is not divisible by 2, 3, 5 or 7 (and \(11^2=121\gt 61\)), so 61 is prime: P(5) is true.
Both P(3) and P(5) are true.
Answer: (2) Both P(3) and P(5) are true
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