- **Math**
(*https://www.mersenneforum.org/forumdisplay.php?f=8*)

- - **Fibonacci sums?**
(*https://www.mersenneforum.org/showthread.php?t=178*)

Fibonacci sums?Is 2^p -1 always the sum of p Fibonacci numbers?
examples: 3=1+2 7=1+1+5 31=2+3+5+8+13 127=1+1+2+13+21+34+55 2047= ...............................? 8191=1+1+5+21+34+55+89+233+377+610+987+1597+4181 I cant seem to find the sum for p=11. :rolleyes: |

Re: Fibonacci sums?[quote="TTn"]Is 2^p -1 always the sum of p Fibonacci numbers?[/quote]
Yes. [quote="TTn"]I cant seem to find the sum for p=11.[/quote] One answer is 2047=2+3+5+8+21+34+55+89+233+610+987. There are more. |

Re: Fibonacci sums?[quote="TTn"]Is 2^p -1 always the sum of p Fibonacci numbers?[/quote]
Okay, lets make it more interesting: Is 2^p - 1 always the sum of p [b]Unique* [/b]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 [b]fewest [/b]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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