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Omni-MATH / For a given positive integer n, we define φ(n) to be the number of positive integers less than or equal to n which share no common prime factors with n. Find all positive integers …

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problem

For a given positive integer nn, we define φ(n)\varphi(n) to be the number of positive integers less than or equal to nn which share no common prime factors with nn. Find all positive integers nn for which φ(2019n)=φ(n2)\varphi(2019 n)=\varphi\left(n^{2}\right).
Plain-text mathematical notation (without MathML)
For a given positive integer n, we define φ(n) to be the number of positive integers less than or equal to n which share no common prime factors with n. Find all positive integers n for which φ(2019n)=φ(n²).
Original LaTeX notation
For a given positive integer $n$, we define $\varphi(n)$ to be the number of positive integers less than or equal to $n$ which share no common prime factors with $n$. Find all positive integers $n$ for which $\varphi(2019 n)=\varphi\left(n^{2}\right)$.

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Source and history

task_id
b8adad4c-f318-548a-8c01-fad304db27ad
task_key
test--b8adad4c-f318-548a-8c01-fad304db27ad
task_revision_id
1
config / split
/ test

Official source

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