01. Increasing multiplicative functions

Happy new year, everyone! In this week, we propose two problems (the first one is easy and the second one is challenging):

01a. PEN K12 (Canada 1969) Find all functions such that for all
: , , .

01b. Let be a function satisfying the conditions:
(a) for all relatively prime and , and
(b) for all positive integers .
Show that there is a constant such that for all .

* Any comments are welcome! You can also disscuss the problems here!
* To get the current edition of PEN Problems Book, visit here!
* Next week, the solutions will be uploaded here in the pdf file.