You're viewing a comment by Peter Krumins and its responses.

January 15, 2010, 07:52

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.

Comment Responses

Shivam Permalink
August 26, 2012, 07:56

I don't understood properly.Can you explain in some other way

Reply To This Comment

(why do I need your e-mail?)

(Your twitter handle, if you have one.)

Type the word "quake3_181": (just to make sure you're a human)

Please preview the comment before submitting to make sure it's OK.