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MATH / For a positive integer n and an angle θ, cosθ is irrational, but cos2θ, cos3θ, …, cosnθ are all rational. Find the largest possible value of n.

Problem

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problem

For a positive integer nn and an angle θ,\theta, cosθ\cos \theta is irrational, but cos2θ,\cos 2 \theta, cos3θ,\cos 3 \theta, …,\dots, cosnθ\cos n \theta are all rational. Find the largest possible value of n.n.
Plain-text mathematical notation (without MathML)
For a positive integer n and an angle θ, cosθ is irrational, but cos2θ, cos3θ, …, cosnθ are all rational.  Find the largest possible value of n.
Original LaTeX notation
For a positive integer $n$ and an angle $\theta,$ $\cos \theta$ is irrational, but $\cos 2 \theta,$ $\cos 3 \theta,$ $\dots,$ $\cos n \theta$ are all rational.  Find the largest possible value of $n.$

level

Level 5

type

Precalculus

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Source and history

task_id
f23abca6-3213-5dbc-bc0a-f5bbb2619de8
task_key
precalculus--test--f23abca6-3213-5dbc-bc0a-f5bbb2619de8
task_revision_id
1
config / split
precalculus / test

Official source

initial import