Revisiting How Many 1’s Are Needed
Abstract
In a contribution to this Quarterly, Rawsthorne considered the problem of determining the minimum number ǁnǁ of copies of 1 needed to express a positive integer n via addition and multiplication. This number ǁnǁ is referred to as the integer complexity of n, and the study of recurrence-related properties of the integer complexity function dates back to the work of Mahler and Popken. Since it is not necessarily the case that ||n||≤||nm|| for positive integers n and m, this leads us to explore the function [[n]]:=min{||nm||:m∈N} introduced in this paper.
Fields of Study & Subjects
Educational Theory and Curriculum Studies
Psychometric Methodologies and Testing
Mathematics Education and Teaching Techniques
Publication details
- Journal / source
- The Fibonacci Quarterly
- Volume
- 64
- Issue
- 3
- Pages
- 510–515
- Publication date
- 5 January 2026
- Language
- EN