The equations with prime moduli always have 2 solutions. The equations with composite moduli have 4 solutions. If there were no mod sign, that would mean:
Example: e) x^2 = 1(mod 21)
It would be:
x^2 = 1 + 21
x^2 – 1 = 21
(x+1)(x-1) = 21
So, the x^2 – 1 would just equal the divisor in mod equations.
This response is written by Yash Agarwal