If p is a prime number greater than 3, then (p²-1) is always divisible by · ABC26GN0302
Subject: General Aptitude · Chapter: Number System
If $p$ is a prime number greater than 3, then $\left(p^{2}-1\right)$ is always divisible by
(a)6 but not 12
(b)12 but not 24
(c)24
(d)None of these
Answer
Answer (as printed): C
Explanation
p = 5 ⇒ (p2 – 1) = (25 – 1) = 24, which is divisible by 24. p = 7 ⇒ (p2 – 1) = (49 – 1) = 48, which is divisible by 24. p = 11 ⇒ (p2 – 1) = (121 – 1) = 120, which is divisible by 24. Hence, (p2 – 1) is always divisible by 24.
Explanation as extracted from the printed page; notation may be imperfect.