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You're replying to a comment by Peter Krumins.
Kou, all numbers can be represented as a sum of Fibonacci numbers.
Proof's really easy: it's true for n=1. Now suppose it's true for all n<=k. If n+1 is Fibonacci number, we are done. Otherwise, this number n+1 is bigger than some Fibonacci number Fi. Now let's look at the number n+1-Fi. As this number is smaller than n+1, then according to the inductive hypothesis it can be expressed as a sum of Fibonacci numbers. Therefore n+1 can be expressed as Fi + (n+1-Fi), where Fi is a Fibonacci number and (n+1-Fi) is a sum of Fibonacci numbers.
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It would be nice if you left your e-mail address. Sometimes I want to send a private message, or just thank for the great comment. Having your e-mail really helps.
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