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Difference between revisions of "2021 WSMO Team Round Problems/Problem 14"

(Created page with "==Problem== Suppose that <math>x</math> is a complex number such that <math>x+\frac{1}{x}=\frac{\sqrt{6}+\sqrt{2}}{2}</math> and the imaginary part of <math>x</math> is nonneg...")
 
(No difference)

Latest revision as of 22:16, 15 December 2023

Problem

Suppose that $x$ is a complex number such that $x+\frac{1}{x}=\frac{\sqrt{6}+\sqrt{2}}{2}$ and the imaginary part of $x$ is nonnegative. Find the sum of the five smallest nonnegative integers $n$ such that $x^{n}+\frac{1}{x^n}$ is an integer.

Proposed by pinkpig

Solution

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