For each positive integer \(n\), the set of integers \(\{0,1,\ldots,n-1\}\) is known as the \(\textit{residue system modulo}\text{ }n.\) Within the residue system modulo \(2^4\), let \(A\) be the sum of all invertible integers modulo \(2^4\) and let \(B\) be the sum all of non-invertible integers modulo \(2^4\). What is \(A-B\)?
1 - The mmi = 1
3 - The mmi = 11
5 - The mmi = 13
7 - The mmi = 7
9 - The mmi = 9
11 - The mmi = 3
13 - The mmi = 5
15 - The mmi = 15
Total of All mmis = 64 - Sum of A of all invertible integers between 1 and 16
2 + 4 + 6 + 8 + 10 + 12 + 14 =56 Sum of B of all non-invertible integers between 1 and 16 inclusive.
Sum A - Sum B =64 - 56 = 8
