# An algebra problem by Justin Tuazon

Algebra Level 4

Let $$P(x)$$ be a polynomial with a degree of 6. $$P(x)$$ satisfies the following conditions: $\begin{cases} P(0)=5041 \\ P(1)=3 \\ P(2)=7 \\ P(3)=13 \\ P(4)=21 \\ P(5)=31 \\ P(6)=43 \\ \end{cases}$

Find the sum of the digits of the value of $$P(9)$$.

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