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 .