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min pos. integer not in form (2^a - 2^b/(2^c - 2^d) (2019 Auckland MO S4)

Source:

November 15, 2021
number theory

Problem Statement

Find 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, b b, cc, dd are non-negative integers.
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