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May 10th, 2013, 01:14 PM  #1 
Senior Member Joined: Feb 2012 Posts: 628 Thanks: 1  A Fibonacci Puzzle
Determine all numbers that can be written in only one way as a sum of distinct Fibonacci numbers. For example, 4 is such a number since it can be written as 1 + 3 but in no other way as a sum of distinct Fibonacci numbers. 6 is not such a number since it can be written as both 1 + 2 + 3 and 1 + 5. 
May 11th, 2013, 08:25 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: A Fibonacci Puzzle
Zeckendorf's theorem is presumably useful here.


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