# Inspired by Mohammad Rasel Parvej

Algebra Level 5

Let $$P(x) \in \mathbb{R}[x]$$ be a Polynomial in x defined as follows: $$P(x) = x^{2016} + x^{2013} + x^{2010} + x^{2007} + ... + x^6 + x^3 +1$$; $$(P: \mathbb{R} \to \mathbb{R})$$

Let $$R(x)=C$$ be the Polynomial that is obtained as remainder when $$P(x)$$ is divided by $$x^3 -3$$

$$C$$ is a Constant Natural Number. Find the number of $$1$$'s in Base-3(ternary base) in the representation of $$C$$.

Inspiration

Bonus: How many 1's would have $$C$$ if $$P : \mathbb{Z}_3 \rightarrow \mathbb{Z}_3$$?

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