Polynomials. Yet Again

Algebra Level 4

\[ \large \begin{cases} {p(1)=1} \\ {p(2)=3} \\ {p(3)=5}\\ {p(4)=7}\\ {p(5)=9} \end{cases} \]

Let \(p(x)\) be a polynomial of degree 5 with leading coefficient as 2009 such that the satisfy the equations above, find the value of \(p(6)\).

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