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.

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