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UKMT Intermediate Mathematical Challenge, 2020

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

The positive integers $m$ and $n$ are such that $10 \times 2^m = 2^n + 2^{n+2}$ . What is the difference between $m$ and $n$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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