# Given a polynomial f(x) of n degree such that f(x)+f(1x)=f(x)⋅f(1/x) Find the polynomial

Given a polynomial $f\left(x\right)$ of n degree such that
$f\left(x\right)+f\left(\frac{1}{x}\right)=f\left(x\right)\cdot f\left(\frac{1}{x}\right)$
Find the polynomial
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driogairea1
$f\left(y\right)=1+y$
$f\left(x\right)+f\left(\frac{1}{x}\right)=1+x+1+\frac{1}{x}=2+x+\frac{1}{x}$
$f\left(x\right)f\left(\frac{1}{x}\right)=\left(1+x\right)\left(1+\frac{1}{x}\right)=1+x+\frac{1}{x}+x\frac{1}{x}=2+x+\frac{1}{x}$
In fact, $f\left(y\right)=1+{y}^{k}$ for $k\in \mathbb{N}$ seems to work for the same reason.