Difference between revisions of "2020 AIME II Problems/Problem 1"
(→Solution) |
|||
Line 6: | Line 6: | ||
~superagh | ~superagh | ||
− | + | <br><br> | |
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 20:38, 7 June 2020
Problem
Find the number of ordered pairs of positive integers such that
.
Solution
First, we find the prime factorization of , which is
. The equation
tells us that we want to select a perfect square factor of
,
.
will be assigned by default. There are
ways to select a perfect square factor of
, thus our answer is
.
~superagh
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.