MathDB
2012 Spring Team #7

Source:

March 20, 2022
number theory

Problem Statement

A positive integer xx is kk-equivocal if there exists two positive integers bb, bb' such that when xx is represented in base bb and base bb', the two representations have digit sequences of length kk that are permutations of each other. The smallest 22-equivocal number is 77, since 77 is 2121 in base 33 and 1212 in base 55. Find the smallest 33-equivocal number.