# Find positive integers $(m,n)$ such $\left[\dfrac{nk}{m}\right]=[\sqrt{2}k]$ [closed]

Are there positive integer numbers $(m,n)$ such that

(1): $gcd(m,n)=1,m\le 2011;$

(2): for any $k=1,2,\cdots,2011,\left[\dfrac{nk}{m}\right]=[\sqrt{2}k]$

where $[x]$ is the largest integer not greater than x.

If they exist, find $(m,n),m,n\in N^{*}$.

-
Contest problem from the year 2011? Presumably (2) should hold for all $k$? –  Jyrki Lahtonen Sep 23 '13 at 6:37