# Cocassi Function Algebra New Year Special

Algebra Level 3

Let $$F(x)$$ denote a monic $$7^\text{th}$$ degree polynomial with satisfying the following

$$F(2) = 2, F(3) = 3, F(4) =4, F(5) = 5, F(6) = 6, F(7) =7, F(8) = 8$$

What is the value of $$F(9) \bmod 7$$?

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