If p is a prime number greater than 3, then (p² - 1) is always divisible by :

A. 6 but not 12

B. 12 but not 24

C. 24

D. None of these

Answer: Option C

Solution(By Examveda Team)

⇔ p = 5
⇒ (p² - 1) = (25 - 1)
⇒ (p² - 1) = 24, which is divisible by 24
⇔ p = 7
⇒ (p² - 1) = (49 - 1)
⇒ (p² - 1) = 48, which is divisible by 24
⇔ p = 11
⇒ (p² - 1) = (121 - 1)
⇒ (p² - 1) = 120, which is divisible by 24
Hence, (p² - 1) is always divisible by 24