Prove p^2-1 is a multiple of 24 ∀ p prime greater than 3 without using modular arithmetic

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[Number Theory] Why is square of a prime (greater than 3) minus 1 always divisible by 24? [Number Theory] Why is square of a prime (greater than 3) minus 1 always divisible by 24?
Proof p^2==1 (modulo 24) for all prime numbers greater than or equal to 5 Proof p^2==1 (modulo 24) for all prime numbers greater than or equal to 5
If \( n \) is a prime number greater than 3 , shew that \( n^{2}-1 \) is a multiple of 24 . If \( n \) is a prime number greater than 3 , shew that \( n^{2}-1 \) is a multiple of 24 .
How to prove p^2-1 is divisible by 24? How to prove p^2-1 is divisible by 24?
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calculate mod (using scientific calculator ). calculate mod (using scientific calculator ).