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Very beautiful NT

Source: 42nd International Tournament of Towns, Senior A-Level P6, Spring 2021

February 18, 2023
number theoryFibonacciTournament of Towns

Problem Statement

Find at least one real number AA{} such that for any positive integer nn{} the distance between ⌈An⌉\lceil A^n\rceil and the nearest square of an integer is equal to two.
Dmitry Krekov
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