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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 \(A-B\)?

 Jan 31, 2020
 #1
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A = 56 and B = 80, so A - B = -24.

 Jan 31, 2020
 #2
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Sorry, but it says it's incorrect. The answer is 8

Guest Jan 31, 2020
 #3
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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 

 Jan 31, 2020

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