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If n is a prime number greater than 3, show that n2 â€“ 1 is divisible by 24

A.	yes	B.	no
C.	Un-determine	D.	None of these

Answer and Explanation

Answer:yes

Explanation:
n2 â€“ 1 = (n + 1) (n â€“ 1)
Every prime number greater than 3 can be written in the form of
(6K + 1) or (6K â€“ 1), where K is a positive integer. Let n = 6K + 1,
then (n + 1) (n â€“ 1) = (6K + 1 + 1) (6K + 1 - 1)
= (6K + 2) (6K)
= 12 K (3K + 1)
Either K or (3K + 1) is even. K (3K + 1) is even.
Since K (3K + 1) is even, it is divisible by 2. Hence, 12 Ã— K(3K + 1) is Divisible by 12 Ã— 2 = 24

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