Re: Is { k^2 * r mod 1 | k is integer} dense in [0,1]?

In article
<9e9e53b6-c234-44ea-939b-229bae7b8ba4@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
misterdonut.chen@xxxxxxxxx wrote:

Let r be an irrational number.
I know and can prove that { k* r mod 1 | k is integer} is dense in
[0,1].
My question is -- Is { (k^2) * r mod 1 | k is integer } dense in
[0,1] ?

I don't know. I'd recommend having a look through
Kuipers & Niederreiter, Uniform Distribution of Sequences.

--
Gerry Myerson (gerry@xxxxxxxxxxxxxxx) (i -> u for email)
.

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