Polynomials. Yet Again

Algebra Level 4

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

Let p(x)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)p(6).

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