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MATH / For each positive integer n, the set of integers {0,1,…,n−1} is known as the textit{residue system modulo} n. Within the residue system modulo 2⁴, let A be the sum of all invertibl…

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problem

For each positive integer nn, the set of integers {0,1,…,n−1}\{0,1,\ldots,n-1\} is known as the $\textit{residue system modulo}$ nn. Within the residue system modulo 242^4, let AA be the sum of all invertible integers modulo 242^4 and let BB be the sum all of non-invertible integers modulo 242^4. What is A−BA-B?
Plain-text mathematical notation (without MathML)
For each positive integer n, the set of integers {0,1,…,n−1} is known as the $\textit{residue system modulo}$ n. Within the residue system modulo 2⁴, let A be the sum of all invertible integers modulo 2⁴ and let B be the sum all of non-invertible integers modulo 2⁴. What is A−B?
Original LaTeX notation
For each positive integer $n$, the set of integers $\{0,1,\ldots,n-1\}$ is known as the $\textit{residue system modulo}$ $n$. 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 $A-B$?

level

Level 5

type

Number Theory

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Source and history

task_id
f08ebe16-94c9-5de2-ba45-9860cdabcbd8
task_key
number~5ftheory--test--f08ebe16-94c9-5de2-ba45-9860cdabcbd8
task_revision_id
1
config / split
number_theory / test

Official source

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