Rose Petals

Algebra Level 1

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

For example, P(4)=8P(4) = 8 because r=cos(4θ)r = \cos(4\theta) has 88 petals, and P(5)=5P(5) = 5 because r=cos(5θ)r = \cos(5\theta) has 55 petals.

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

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