Let $x_t$ and $y_t$ real periodic sequences such that the least common multiple of their periods exists. Then, given a constant $a$, $x_t+ay_t$ is also periodic with period, say, $p$. Does $x_t-ay_t$ also need to have period $p$? Thanks in advance. Observations Let $p_1$ be the fundamental perio...

This question is related to this, where a simple counter-example was given to show a negative answer. Let $x_t$ and $y_t$ real periodic sequences such that the least common multiple of their periods exists. Then, given a constant $a$, $x_t+ay_t$ is also periodic with period, say, $p$. Under whic...