Problem Solving

If p ≥ 5 is a prime number, then the remainder when p^2 -1 is divided by 24 is:

A. 0

B. 1

C. 2

D. 3

E. 4

IMO A.

p^2-1 (when p>=5) will be multiple of 24, so the reminder will be 0.

Whatever be the answer, one thing that it shows that any prime getter than 3 will have one multiple of 3 and 3 multiples of 2 one unit away? interesting properties, any idea why?

I can think this one is related to the properties of (n-1)n(n+1) here n is not an multiple of 2/3 as it is prime, so out of these three consecutive numbers one will be guaranteed to be a multiple of 3, at the same time since both the number away at one place will be a multiple of 2(even no) also all the consecutive even nos will have one more 2 so the third onbe here..wow...wonder