MathDB
Sequence from non-integer x is not periodic

Source: Japanese MO Finals 1996

February 11, 2011
floor functionalgebra proposedalgebra

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.
Back to ProblemsView on AoPS