2002 AIME II Problems/Problem 3
From AoPSWiki
Problem
It is given that 
where 
and 
are positive integers that form an increasing geometric sequence and 
is the square of an integer. Find 
Solution
. Since they form an increasing geometric sequence, 
is the geometric mean of the product 
. ![b=\sqrt[3]{abc}=6^2=36](http://alt1.artofproblemsolving.com/Forum/latexrender/pictures/0/6/e/06ed086b27b362a57cb6e23063cc7afaef84c413.gif)
.
Since is the square of an integer, we can find a few values of 
that work: 11, 20, 27, 32, and 35. 11 doesn't work. Nor do 20, 32, or 35. Thus, 
, and 
.
See also
| 2002 AIME II (Problems • Resources) | ||
| Preceded by Problem 2 | Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
