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Omni-MATH / An integer n is chosen uniformly at random from the set {1,2,3,…,2023!}. Compute the probability that gcd(n^(n)+50,n+1)=1

Problem

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problem

An integer nn is chosen uniformly at random from the set {1,2,3,…,2023!}\{1,2,3, \ldots, 2023!\}. Compute the probability that gcd(nn+50,n+1)=1\operatorname{gcd}\left(n^{n}+50, n+1\right)=1
Plain-text mathematical notation (without MathML)
An integer n is chosen uniformly at random from the set {1,2,3,…,2023!}. Compute the probability that gcd(n^(n)+50,n+1)=1
Original LaTeX notation
An integer $n$ is chosen uniformly at random from the set $\{1,2,3, \ldots, 2023!\}$. Compute the probability that $$\operatorname{gcd}\left(n^{n}+50, n+1\right)=1$$

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Source and history

task_id
9c16a546-cbe0-5e05-b33f-70ac4278c6c0
task_key
test--9c16a546-cbe0-5e05-b33f-70ac4278c6c0
task_revision_id
1
config / split
/ test

Official source

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