Let-p-be-a-prime-number-greater-than-3-Prove-that-p-2-1-is-always-divisible-by-24-

Question Number 216875 by ArshadS last updated on 23/Feb/25

Let p be a prime number greater than 3 . Prove that p^{2} - 1

is always divisible by 24 .

Answered by maths2 last updated on 23/Feb/25

(p - 1) (p + 1)

3 ∣ (p - 1) (p + 1); s i n c e p \equiv 1, 2 [3]

p \equiv 1, 3, 5, 7 [8]

\Rightarrow p^{2} \equiv 1 [8] \Rightarrow 8 ∣ p^{2} - 1

s i n c e 3 a n d 8 a r e c o p r i m 3.8 = 24 ∣ p^{2} - 1

Commented by ArshadS last updated on 23/Feb/25

N i c e! T h a n k s s i r!

Facebook Tweet Pin