MathDB
G 20

Source:

May 25, 2007
floor functionlogarithmsIrrational numbers

Problem Statement

You are given three lists A, B, and C. List A contains the numbers of the form 10k10^{k} in base 10, with kk any integer greater than or equal to 1. Lists B and C contain the same numbers translated into base 2 and 5 respectively: ABC1010102010011001004001000111110100013000.\begin{array}{lll}A & B & C \\ 10 & 1010 & 20 \\ 100 & 1100100 & 400 \\ 1000 & 1111101000 & 13000 \\ \vdots & \vdots & \vdots \end{array}. Prove that for every integer n>1n > 1, there is exactly one number in exactly one of the lists B or C that has exactly nn digits.