Many square brackets

Algebra Level 4

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

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