Problem #PRU-73648

Problemas Teoría de números Sistemas numéricos Sistema de números decimales Métodos Principio del casillero Principio del casillero (otro)
 13–15  4.0

Problem

Prove that for any positive integer \(n\), it is always possible to find a number, consisting of the digits \(1\) and \(2,\) that is divisible by \(2^n\). (For example, \(2\) is divisible by \(2\), \(12\) is divisible by \(4,\) \(112\) is divisible by \(8,\) \(2112\) is divisible by \(16\) and so on...).