Group (mathematics)
In modular arithmetic, two integers are added and then the sum is divided by a positive integer called the modulus. The result of modular addition is the remainder of that division. For any modulus, n, the set of integers from 0 to n - 1 forms a group under modular addition: the inverse of any element a is n - a, and 0 is the identity element. This is familiar from the addition of hours on the face of a clock: if the hour hand is on 9 and is advanced 4 hours, it ends up on 1, as shown at the right. This is expressed by saying that 9 + 4 equals 1 "modulo 12" or, in symbols,
What positive integer is used to divide the sum of two positive integers in modular mathematics?
the modulus
In modular arithmetic, two integers are added and then the sum is divided by a positive integer called the modulus.
the sum