It is not difficult to show (even without Weyl criterion) that the sequence $\sqrt{n}$, $n=1,2,\ldots$ is equidistributed mod 1. However, I need a reference to this result. Can you help me? Thanks.



References for the result that $\sqrt{n}$ is equidistributed mod 1
Fejer's theorem: If $w(t)$ is a function with continuous first and second derivatives whose signs are eventually constant, and if $t \cdot w'(t)$ goes to infinity for $t$ to infinity, and $w(t)/t$ goes to zero, then $(w(n): n=1,2,3,...)$ is uniformly distributed. 


In particular, for any fixed $b>0$ and $\alpha$ between $0$ and $1$, $b\cdot n^\alpha$ is uniformly distributed. 


Reference: 
Hlawka, The theory of uniform distribution, page 23. Certainly also in Kuipers-Niederreiter, which I do not have here at the moment. 
(EDIT: After a bit of prodding, Google helped me to find Theorem 2.5 on page 13 in Kuipers-Niederreiter: If the sequence of differences $b\_n:=a\_{n+1}-a\_n$ converges monotonically to zero, and $n b\_n$ diverges to infinity, then $a\_n$ is u.d. mod 1.)


