Problem:
The functions and are periodic with least period . What is the least period of the function ?
Answer Choices:
A.
B.
C.
D.
E. It's not periodic.
Solution:
Because , the function is periodic with period . Furthermore, if and only if , which occurs if and only if is a multiple of , so the period cannot be less than . Therefore the function has least period .
The problems on this page are the property of the MAA's American Mathematics Competitions