MathDB
Periodic Sequence

Source: Japan Final MO

March 26, 2020
number theoryalgebranumber theory unsolvedSequencealgebra unsolved

Problem Statement

Let x>1x>1 be a real number which is not an integer. For each n∈Nn\in\mathbb{N}, let an=⌊xn+1⌋−x⌊xn⌋a_n=\lfloor x^{n+1}\rfloor - x\lfloor x^n\rfloor. Prove that the sequence (an)(a_n) is not periodic.
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