How to add two natural numbers in base PHI

F. Michel Dekking*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
8 Downloads (Pure)


In the base phi representation, any natural number is written uniquely as a sum of powers of the golden mean with coefficients 0 and 1, where it is required that the product of two consecutive digits is always 0. In this self-contained paper, we give a new and short proof of the recursive structure of the base phi representations of the natural numbers.

Original languageEnglish
Pages (from-to)19-22
Number of pages4
JournalFibonacci Quarterly
Issue number1
Publication statusPublished - 2021


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