Talk:2007 AIME II Problems/Problem 14
Revision as of 08:16, 17 March 2008 by ZHANGWENZHONGKK (talk | contribs)
Here is a completed solution to 2007AIMEII-14. Let .$\[f\left( 0 \right) = 1 \Rightarrow a_0 = 1 \]$ (Error compiling LaTeX. Unknown error_msg).. or (impossible). Let . Then and the same thing got:$\[f_1 \left( x \right) \equiv 1 \]$ (Error compiling LaTeX. Unknown error_msg) 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. Unknown error_msg) such that .Then $\f_n \left( x \right) = 1{\rm{ or }}x + 1 $ (Error compiling LaTeX. Unknown error_msg).Check if and we can easily get and and .