We say that $ a$ and $ b$ are inverses modulo $ n$, if $ ab \ equiv 1 \ mod n$, and we might write $ b = a^ { - 1} $. for example, you’ re calculating 15 mod 4. the modulo operation finds the remainder of a divided by b. for example $ 17\ cdot 113 = 1921 = 120\ cdot 16 + 1 \ equiv 1 \ mod 120$, so $ 17^ { - 1} = 113$ modulo $ 120$. note: possible remainders of n are 0,. the term modular arithmetic is used to refer to the operations of addition and multiplication of congruence classes in the integers modulo n. addition and multiplication in zn are defined as follows: for [ a], [ c] ∈ zn, [ a] ⊕ [ c] = [ a + c] and [ a] modulo ■ [ c] = [ ac]. 27 ÷ 6 = 4 with a remainder of 3; 27 mod 6 = 3; example modulo calculation. theorem 1 : two integers a and b are said to be congruent modulo n, a ≡ b( modn), if all of the following are true: a) m ■ ( a b). in mathematics, the term modulo ( " with respect to a modulus of", the latin ablative of modulus which itself means " a small measure" ) is often used to assert that two distinct mathematical objects can be regarded as equivalent— if their difference is accounted for by an additional factor. to do this by hand just divide two numbers and note the remainder. modulo is also referred to as ‘ mod. how to do a modulo calculation.
b) both a and b have the same remainder when divided by n. c) a b = kn, for some k ∈ z. another example: equals 2 because 14/ 12 = 1 with a remainder of 2. when you divide 15 by 4, there’ s a remainder. in mathematics, the modulo is the remainder or the number that’ s left after a number is divided by another value. 12- hour time uses moduloo' clock becomes 2 o' clock) it is where we end up, not how many times around. if you needed to find 27 mod 6, divide 27 by 6. example: 100 mod 9 equals 1 because 100/ 9 = 11 with a remainder of 1.
’ the standard format for mod is: a mod n where a is the value that is divided by n. the modulo ( or " modulus" or " mod" ) is the remainder after dividing one number by another.