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Omni-MATH / Define φ^(k)(n) as the number of positive integers that are less than or equal to n/k and relatively prime to n. Find ϕ²⁰⁰¹(2002²−1). (Hint: ϕ(2003)=2002.)

Problem

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problem

Define φk(n)\varphi^{k}(n) as the number of positive integers that are less than or equal to n/kn / k and relatively prime to nn. Find ϕ2001(20022−1)\phi^{2001}\left(2002^{2}-1\right). (Hint: ϕ(2003)=2002\phi(2003)=2002.)
Plain-text mathematical notation (without MathML)
Define φ^(k)(n) as the number of positive integers that are less than or equal to n/k and relatively prime to n. Find ϕ²⁰⁰¹(2002²−1). (Hint: ϕ(2003)=2002.)
Original LaTeX notation
Define $\varphi^{k}(n)$ as the number of positive integers that are less than or equal to $n / k$ and relatively prime to $n$. Find $\phi^{2001}\left(2002^{2}-1\right)$. (Hint: $\phi(2003)=2002$.)

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Source and history

task_id
276eb988-861d-5d26-85cf-76a64ff2cd9f
task_key
test--276eb988-861d-5d26-85cf-76a64ff2cd9f
task_revision_id
1
config / split
/ test

Official source

initial import