Difference between revisions of "2020 AIME II Problems/Problem 1"
Topnotchmath (talk | contribs) m |
Topnotchmath (talk | contribs) m |
||
Line 9: | Line 9: | ||
[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] | ||
==See Also== | ==See Also== | ||
− | {{AIME box|year=2020|n=II| | + | {{AIME box|year=2020|n=II|before=First Problem|num-a=2}} |
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 23:04, 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
See Also
2020 AIME II (Problems • Answer Key • Resources) | ||
Preceded by First Problem |
Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.