Home Competitions AUSTRIAN-POLISH 1999 Problem 3
AUSTRIAN-POLISH 1999 Problem 3
Given an integer n ≥ 2 n \ge 2 n ≥ 2 n n n f 1 , . . . , f n : R → R f_1,..., f_n : R \to R f 1 , ... , f n : R → R x , y ∈ R x,y \in R x , y ∈ R { f 1 ( x ) − f 2 ( x ) f 2 ( y ) + f 1 ( y ) = 0 f 2 ( x 2 ) − f 3 ( x ) f 3 ( y ) + f 2 ( y 2 ) = 0... f n ( x n ) − f 1 ( x ) f 1 ( y ) + f n ( y n ) = 0 \begin{cases} f_1(x)-f_2 (x)f_2(y)+ f_1(y) = 0 f_2(x^2)-f_3 (x)f_3(y)+ f_2(y^2) = 0 ... f_n(x^n)-f_1 (x)f_1(y)+ f_n(y^n) = 0 \end {cases} { f 1 ( x ) − f 2 ( x ) f 2 ( y ) + f 1 ( y ) = 0 f 2 ( x 2 ) − f 3 ( x ) f 3 ( y ) + f 2 ( y 2 ) = 0... f n ( x n ) − f 1 ( x ) f 1 ( y ) + f n ( y n ) = 0
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