Problem #PRU-73648

Problems Number Theory Numeral systems Decimal number system Methods Pigeonhole principle Pigeonhole principle (other)

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...).

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