Lounie G.

asked • 03/21/18

How to prove distinct Fibonacci numbers

8) How to prove that every positive integer can be written as the sum of one or more distinct non-consecutive Fibonacci numbers?

9) How to prove that the sum of any set of distinct non-consecutive Fibonacci numbers whose largest member is Fk is strictly less than Fk+1?

10) How to prove that no positive integer can be written in two different ways as the sum of distinct non-consecutive Fibonacci numbers?

11) How to show that the set of positive integers can be partitioned into Fibonacci sets (i.e. there's a collection of Fibonacci sets so that every positive integer is in precisely one of them) by referencing questions 8 and 10?

1 Expert Answer


Kenneth S. answered • 03/21/18

4.8 (62)

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