MathDB

Multiples of 2^n with n digits, all of them being 1 or 2

Source: Bundeswettbewerb Mathematik 1973, round 2, problem 4

May 1, 2007

Problem Statement

Prove: for every positive integer there exists a positive integer having n digits, all of them being

1

's and

2

's only, such that this number is divisible by

2^{n}

. Is this still true in base

4

6