2007 AIME I Problems/Problem 1
Problem
How many positive perfect squares less than 
are multiples of 
?
Solution
The prime factorization of is 
; thus each square must have 3 factors of 
and 1 factor of 
. This means that the square is in the form 
, where c is a positive integer. There are 
solutions.
See also
| 2007 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
