Rose Petals

Algebra Level 1

\(P(k)\) is the number of petals in a rose formed by the polar equation \(r = \cos(k\theta).\)

For example, \(P(4) = 8\) because \(r = \cos(4\theta)\) has \(8\) petals, and \(P(5) = 5\) because \(r = \cos(5\theta)\) has \(5\) petals.

Is there a positive integer \(k\) such that \(P(k) = 2018?\)

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