Thread: Fibonacci sums?
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Old 2002-10-25, 21:47   #3
Maybeso's Avatar
Aug 2002
Portland, OR USA

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Default Re: Fibonacci sums?

Originally Posted by TTn
Is 2^p -1 always the sum of p Fibonacci numbers?
Okay, lets make it more interesting:

Is 2^p - 1 always the sum of p Unique* Fibonacci numbers?
*(unique as in use each number once)

The smaller p will be difficult:
7 = 1+1+5 = 2+2+3 ... I see no solution for 3.

To prove or disprove either of these questions, it is sufficient to find the fewest q < p Fibonacci numbers needed to sum each Mp.
i.e. if you can always express Mp as the sum of 5 Fn, then you can replace F(n) with F(n-1) + F(n-2), then repeat the process until you have p numbers.
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