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2021 Alg/NT Div 1 P8

Source:

March 2, 2021

algebranumber theory

Problem Statement

There are integers

v,w,x,y,z

and real numbers

0\le \theta < \theta' \le \pi

such that

\cos 3\theta = \cos 3\theta' = v^{-1}, \qquad w+x\cos \theta + y\cos 2\theta = z\cos \theta'.

Given that

z\ne 0

and

v

is positive, find the sum of the

4

smallest possible values of

v

.
Proposed by Vijay Srinivasan

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