1996 Putnam A6

Let $c>0$ be a constant. Give a complete description, with proof, of

the set of all continuous functions $f: R \to R$ such that $f(x) =

f(x^2+c)$for all$x \in R$. Note that$R$ denotes the set of real numbers.

设 $c>0$ 为常数。给出完整的描述并附上证明

所有连续函数 $f: R \to R$ 的集合，使得 $f(x) =

f(x^2+c)$对于所有$x \in R$。请注意，$R$ 表示实数集。