MathDB
300 degree

Source: 2016 Taiwan TST Round 3

July 25, 2016
number theory

Problem Statement

Let λ\lambda be a positive real number satisfying λ=λ2/3+1\lambda=\lambda^{2/3}+1. Show that there exists a positive integer MM such that ∣M−λ300∣<4−100|M-\lambda^{300}|<4^{-100}.
Proposed by Evan Chen
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