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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_22 / Let f be the unique function defined on the positive integers such that ∑_(d∣n)d⋅f((n)/(d))=1 for all positive integers n. What is f(2023)?

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Let

f

be the unique function defined on the positive integers such that

\sum_{d\mid n}d\cdot f\left(\frac{n}{d}\right)=1

for all positive integers

n

. What is

f(2023)

Plain-text mathematical notation (without MathML)

Let f be the unique function defined on the positive integers such that ∑_(d∣n)d⋅f((n)/(d))=1 for all positive integers n. What is f(2023)?

Original LaTeX notation

Let $f$ be the unique function defined on the positive integers such that \[\sum_{d\mid n}d\cdot f\left(\frac{n}{d}\right)=1\] for all positive integers $n$. What is $f(2023)$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_22
task_id: 9b3d4162-0a95-52b7-8240-64a4f2a68d52
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12A~5fProblems~2fProblem~5f22
task_revision_id: 2
config / split: default / train

Official source

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