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