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typo edited
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edit approved May 27, 2014 at 15:08
user21574
edit approved May 27, 2014 at 15:08
user21574

Let [a]$[a]$ denote the integral part of a real number a$a$. Let a$a$ be an irrational number and b$b$ a real number greater than 1$1$. Consider the sequence (b^n(na-[na]))$(b^n(na-[na]))$ with n$n$ running on the positive integers. I would like to know if this sequence diverges. In other words I want to know if the inverse of the sequence of truncations (na-[na])$(na-[na])$ growths slower than any exponentional sequence.

Let [a] denote the integral part of a real number a. Let a be an irrational number and b a real number greater than 1. Consider the sequence (b^n(na-[na])) with n running on the positive integers. I would like to know if this sequence diverges. In other words I want to know if the inverse of the sequence of truncations (na-[na]) growths slower than any exponentional sequence.

Let $[a]$ denote the integral part of a real number $a$. Let $a$ be an irrational number and $b$ a real number greater than $1$. Consider the sequence $(b^n(na-[na]))$ with $n$ running on the positive integers. I would like to know if this sequence diverges. In other words I want to know if the inverse of the sequence of truncations $(na-[na])$ growths slower than any exponentional sequence.

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Ángel del Río
Ángel del Río
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Growth of the truncation of the integral multiples of an irrational number

Let [a] denote the integral part of a real number a. Let a be an irrational number and b a real number greater than 1. Consider the sequence (b^n(na-[na])) with n running on the positive integers. I would like to know if this sequence diverges. In other words I want to know if the inverse of the sequence of truncations (na-[na]) growths slower than any exponentional sequence.