HMMT February

Algebra Difficulty 4.9 AIME Find the answer

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 $n>0, F_{n}=F_{n+t}$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

60.

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