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min pos. integer in form (2^a - 2^b)/(2^c - 2^d) is odd (2019 Auckland MO J3)

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November 14, 2021
oddnumber theory

Problem Statement

Let xx be the smallest positive integer that cannot be expressed in the form 2a−2b2c−2d\frac{2^a - 2^b}{2^c - 2^d}, where aa, bb, cc, dd are non-negative integers. Prove that xx is odd.
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