A counterexample to the prime conjecture of expressing numbers using just ones

JOURNAL OF NUMBER THEORY

卷:133

Article

Wang, Venecia

关键词: Expressing numbers by ones;    Integer complexity;    Counterexample;    Prime;   

DOI  :  10.1016/j.jnt.2012.08.003

来源: Elsevier

【 摘 要 】

Text. Let f(n) be the least number of ones that can be used to represent n using ones and any number of + and x signs (and parentheses). It is always true that for a prime p, f(p) = f (p - 1) + 1? It's in the famous book Unsolved Problems in Number Theory as problem F26 written by R.K. Guy. The aim of our work is to give a counterexample to the conjecture and some properties on f (n). Video. For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=R8IQI_dwaJE. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free