Problem:
How many positive perfect squares less than are multiples of ?
Solution:
Because , a square is divisible by if and only if it is divisible by . Furthermore, a perfect square less than is a multiple of if and only if is a multiple of less than . Because is the largest multiple of less than , there are such positive integers less than and positive perfect squares which are multiples of .
The problems on this page are the property of the MAA's American Mathematics Competitions