Let R represent the function that, given two inputs, a and b, returns the remainder of a when divided by b. E.g.:
if $$a = bx + c$$, then $$R(a, x) = c$$
This remainder function has a lot of properties. For example, one property says that $$R(a, x)*R(b, x) = R(a*b, x)$$ and that implies another property $$R(a, x)*R(a, x) = R(a^2, x)$$ Is there any similar property that allow us to compute the condition?: $$R(a, x^2)$$