I am self studying Apostol Introduction to analytic number theory and got struck on this problem on page248 and need help.
I am trying general part not the part with 2 summations .
Attempt: Denoting $(m_1,..., m_r) $ by x I can write the summation in image as $\sum_{m_1}^{\infty} ... \sum_{m_r}^{\infty} I(x) {m_1}^{-s_1} ×... {m_r}^{-s_r}$ .
I can't think of anything else. I know I have worked myself only 1 line but I am at loss of ideas for this question and is struck badly.
So, it's my request to kindly help in proving it.
Thank you.