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0551 number theory 5th edition Round 5 p1

Source:

May 6, 2021
number theory5th edition

Problem Statement

Find all real numbers a>1a > 1 such that there exists an integer k≥1k \ge 1 such that the sequence {xn}n≥1\{x_n\}_{n\ge 1} formed with the first kk digits of the number ⌊an⌋\lfloor a^n\rfloor is periodical.
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