3.9, due on October 12

The Cool

I think it's cool that finding the factors of n is just as easy as finding the solutions of a square exponent. 

The Hard

For 5 mod 11, why is (p + 1)/4 = 3? I would think that 5 is our prime, so (5+1)/4 = 3/2, not 3. Then I thought that if p = 11, then (11+1)/4 = 3, but I'm not sure if I'm right.

Also, I don't really understand why 2 has no square root in mod 11 and why it matters if the number is negative or positive.