Many square brackets

Algebra Level 3

$t(x) = \lfloor x\rfloor+\lfloor 2x\rfloor+\lfloor 3x\rfloor+\cdots + \lfloor \phi x\rfloor - \frac{\phi(\phi + 1)}2 x$

Find the fundamental period of the function $t(x)$ given that $\phi$ is a positive integer.