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Fraction is power of two

Source: Romanian District MO 2008, Grade 9, Problem 3

April 30, 2008
floor functionnumber theory proposednumber theory

Problem Statement

Prove that if n≥4 n\geq 4, n∈Z n\in\mathbb Z and ⌊2nn⌋ \left \lfloor \frac {2^n}{n} \right\rfloor is a power of 2, then n n is also a power of 2.
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