2007 AIME I Problems/Problem 1
Revision as of 18:23, 9 January 2022 by Fuzimiao2013 (talk | contribs) (Removed Solution 2 because it's literally just the answer, with no details.)
Problem
How many positive perfect squares less than are multiples of
?
Solution
The prime factorization of is
. Thus, each square must have at least
factors of
and
factor of
and its square root must have
factors of
and
factor of
.
This means that each square is in the form
, where
is a positive integer less than
. 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 |
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