Modular arithmetic for a modulus n defines any two elements a and b that differ by a multiple of n to be equivalent, denoted by ⁠ a ≡ ≡ b ( mod n ) ⁠. Every integer is equivalent to one of the integers from 0 to ⁠ n − − 1 ⁠, and the operations of modular arithmetic modify normal arithmetic by replacing the result of any operation by its equivalent representative. Modular addition, defined in this way for the integers from 0 to ⁠ n − − 1 ⁠, forms a group, denoted as Z n or ⁠ ( Z / n Z , + ) ⁠, with 0 as the identity element and n − − a as the inverse element of ⁠ a ⁠.