I've been looking at this problem trying to figure it out for awhile, but haven't been able to come up with a distinct proof of this:(adsbygoogle = window.adsbygoogle || []).push({});

Do you think it's possible to express every positive integer as the sum of non-consecutive Fibonacci numbers? For example, 20 = 13 + 5 + 2, 33 = 21 + 8 + 3 + 1, and 34 = 34.

I worked through some of this and came to the conclusion that for some numbers, the Fibonacci number directly below the chosen positive integer will always be used in the sum.

[itex] 33 = F_8 + F_6 + F_4 + F_2 = 21 + 8 + 3 + 1. [/itex]

Any suggestions?

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# Non-Consecutive Fibonacci Numbers

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