回復 1# tsyr 的帖子
令\(f\left( 1 \right)=k>-1,k\ne 0\)
\(\begin{align}
& f\left( 1 \right)\times f\left( f\left( 1 \right)+1 \right)=1 \\
& k\times f\left( k+1 \right)=1 \\
& f\left( k+1 \right)=\frac{1}{k} \\
& \\
& f\left( k+1 \right)\times f\left( f\left( k+1 \right)+\frac{1}{k+1} \right)=1 \\
& f\left( \frac{1}{k}+\frac{1}{k+1} \right)=\frac{1}{f\left( k+1 \right)}=k=f\left( 1 \right) \\
& \frac{1}{k}+\frac{1}{k+1}=1 \\
& k=\frac{1\pm \sqrt{5}}{2} \\
\end{align}\)
\(k=\frac{1+\sqrt{5}}{2}\)不合，為什麼不合，就留給您了
