proving that no positive integer can be written in two different ways as the sum of distinct non-consecutive Fibonacci numbers

Asked Mar 23 '18 at 03:35

Active Mar 26 '18 at 05:00

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

edited Mar 26 '18 at 05:00

Eric Wofsey

asked Mar 23 '18 at 03:35

Lounie Germain

Have you tried computing the Fibonacci representation of some concrete numbers, like $20, 50, 100$? – Jalex Stark Mar 23 '18 at 04:27
I did, but I'm having trouble with writing the proof. – Lounie Germain Mar 23 '18 at 11:46

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