The inverse of the multiplication module 37 is: The two values are multiplied with modul 37. The inverse is the rest of the division when the division it's iqual to 1, because 1 it's a neutral element of the multiplication. Example: 5 mod 37 = 5 because 5 it's the rest of division. 15 mod 37 = 15 But (4*15)mod 37 = 75 mod(37) = 1. The inverse of the 5 it's 15 because mod(5 mod 37 * 15 mod 37) = 1 Zero has no inverse because it is not an element of the list.