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Representation as a sum of simple positive integers

Source: Nordic MO 2010 Q4

April 21, 2013
number theory unsolvednumber theory

Problem Statement

A positive integer is called simple if its ordinary decimal representation consists entirely of zeroes and ones. Find the least positive integer kk such that each positive integer nn can be written as n=a1±a2±a3±⋯±akn = a_1 \pm a_2 \pm a_3 \pm \cdots \pm a_k where a1,…,aka_1, \dots , a_k are simple.
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