Quote:
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(n1) + F(n2), then repeat the process until you have p numbers.