Zeckendorf’s Theorem

https://commons.wikimedia.org/wiki/File:Zeckendorf_representations_89px.png

Every positive integer can be represented uniquely as the sum of one or more distinct Fibonacci numbers in such a way that the sum does not include any two consecutive Fibonacci numbers.

Above, 51 = 34 + 13 + 3 + 1.

Discovered in 1952 by Dutch mathematician Gerrit Lekkerkerker (and remarked 20 years later by Edouard Zeckendorf).