Find all real number a  such that for any positive integer n,
$\lfloor \alpha \rfloor +\lfloor 2\alpha \rfloor +\cdots +\lfloor n\alpha \rfloor$
is a multiple of n$\frac{}{}$

$(Note that \lfloor z\rfloor denotes the greatest integer less than or equal to z.For example, \lfloor -\pi \rfloor =-4 and \lfloor 2\rfloor =\lfloor 2.9\rfloor =2.)$

Proposed by Santiago Rodríguez, Colombia