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.

t

is not periodic

\dfrac{1}{\phi}

\phi

1 solution

Guru Prasaadh
Aug 7, 2015

these whole terms give you fractional part of x which is periodic with fundamental period 1