Q509
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
AnswerD.
None of these
Answer: Option C
Solution
Answer: Option C
Solution:
⇔ 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