Question

Why square of a prime number when divided by 12 gives remainder 1?

Answer 1

p2−1=(p−1)(p+1) . Since p is odd, these are two even factors, so the product is divisible by 4. Also, one of p-1, p, p+1 must be divisible by 3, but since p is prime, it is not divisible by 3. Thus one of p-1, or p+1 must be divisible by three