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, 2016

Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The positive integer $N$ has five digits. The six-digit integer $P$ is formed by appending the digit $2$ to the front of $N$ . The six-digit integer $Q$ is formed by appending the digit $2$ to the end of $N$ . Given that $Q = 3P$ , what values of $N$ are possible?

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