HMMT 2001 U50

The Fibonacci sequence $F_{1}, F_{2}, F_{3}, \ldots$ is defined by $F_{1}=F_{2}=1$ and $F_{n+2}=$ $F_{n+1}+F_{n}$. Find the least positive integer $t$ such that for all $n>0, F_{n}=F_{n+t}$.