Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

4. Let $u_{k}$ denote the $k$ th Fibonaccci number. Find the simple continued fraction, terminating with the partial quotient of one, of $u_{k+1} / u_{k}$ , where $k$ is a positive integer.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.