Question 81
Let $f_{1}=0$, $f_{2}=1$, and $f_{n+2}=f_{n+1}+f_{n}$, for $n=1,2, \ldots$, be the Fibonacci sequence. Show that there exists a strictly increasing infinite arithmetic sequence none of whose numbers belongs to the Fibonacci sequence. [A sequence is arithmetic, if the difference of any of its consecutive terms is a constant.]