# Talk:2007 AIME II Problems/Problem 14

Here is a completed solution to 2007AIMEII-14. Let .$\[f\left( 0 \right) = 1 \Rightarrow a_0 = 1 \]$ (Error compiling LaTeX. ! LaTeX Error: Bad math environment delimiter.).. or (impossible). Let . Then and the same thing got:$\[f_1 \left( x \right) \equiv 1 \]$ (Error compiling LaTeX. ! LaTeX Error: Bad math environment delimiter.) or . Let be an integer and $\[f_n \left( x \right) = \frac{{f\left( x \right)}}{{\left( {x^2 + 1} \right)^n }}$ (Error compiling LaTeX. ! LaTeX Error: Bad math environment delimiter.) such that $\[deg f_n \left( x \right) = 0{\text{ or }}1$ (Error compiling LaTeX. ! LaTeX Error: Bad math environment delimiter.).Then $\[f_n \left( x \right) = 1{\rm{ or }}x + 1]$ (Error compiling LaTeX. ! LaTeX Error: Bad math environment delimiter.).Check if and we can easily get and and .