Coprime: number does NOT have common divisor against the modular number.
Coprime Class: The congruence class/set/group which its member is coprime to the modular number.
Coprime order: the cycle length/period of remainder repetition of its exponents mod against the modular number, e.g. member n and modular m, n^i mod m where (i=0:m). The maximum value is called the order/size of the coprime class;
Prime Root: The coprime member number whose coprime order equals to the size of the coprime class.
Quadratic Residue: x an integer is in the range 0:n, r = x^2 mod n, r is quadratic residue if r is one of x.