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**Jameson** Define f: (N U {0}) -> N by $\displaystyle f(n) = 10^n + 3*4^{n+2}+5$ Prove that for all non-negative numbers, n, f(n) divides 9.

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Ok so for this one P(n) is going to be the statement "f(n) divides 9". P(0) holds and we can now assume that this holds true for all j<k.

This part of induction always gets me, now I have to show P(j) -> P(k), or P(n) -> P(n+1).

If f(j) divides 9, then there is some number, D, such that $\displaystyle 9*D = 10^j + 3*4^{j+2}+5$. Now I know there's some way to manipulate this to get what I need but I don't see it.

Hints?