Give a positive integer $\displaystyle n>1$. Let $\displaystyle f_{i}(x) = a_{i}x+b_{i},i = 1,2,3$,nonzero,real polynomial. we have$\displaystyle {f_{1}(x)}^n + {f_{2}(x)}^n = {f_{3}(x)}^n$ . Show that there exist a real polynomial such that $\displaystyle f_{i}(x) = c_{i}f(x)$,where $\displaystyle c_{1},c_{2},c_{3}$ is real numbers.