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MATH / Let a=(π)/(2008). Find the smallest positive integer n such that

Problem

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

problem

Let a=π2008a = \frac{\pi}{2008}. Find the smallest positive integer nn such that ∑k=1n2cos(k2a)sin(ka)\sum_{k = 1}^n 2 \cos (k^2 a) \sin (ka)is an integer.
Plain-text mathematical notation (without MathML)
Let a=(π)/(2008). Find the smallest positive integer n such that
∑_(k=1)^(n)2cos(k²a)sin(ka)is an integer.
Original LaTeX notation
Let $a = \frac{\pi}{2008}$. Find the smallest positive integer $n$ such that
\[\sum_{k = 1}^n 2 \cos (k^2 a) \sin (ka)\]is an integer.

level

Level 4

type

Precalculus

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Source and history

task_id
7662528d-4363-535b-8310-8bd9d735a4d8
task_key
precalculus--test--7662528d-4363-535b-8310-8bd9d735a4d8
task_revision_id
1
config / split
precalculus / test

Official source

initial import