2008 Putnam A5

Let $n \geq 3$ be an integer. Let $f(x)$ and $g(x)$ be polynomials

with real coefficients such that the points

$(f(1), g(1)), (f(2), g(2)), \dots, (f(n), g(n))$

in $\mathbb{R}^2$ are the vertices of a regular $n$-gon in

counterclockwise order. Prove that at least one of $f(x)$

and $g(x)$ has degree greater than or equal to $n-1$.

设 $n \geq 3$ 为整数。设$f(x)$和$g(x)$为多项式

具有实数系数，使得点

$(f(1), g(1)), (f(2), g(2)), \点, (f(n), g(n))$

$\mathbb{R}^2$ 是正则 $n$-gon 的顶点

逆时针顺序。证明至少$f(x)$之一

并且 $g(x)$ 的度数大于或等于 $n-1$。