2002 AIME II Problems/Problem 3
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
.
.
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 $c=\dfrac{36}{27}\cdot 36=\dfrac{4}{3}\cdot 36}=48$ (Error compiling LaTeX. Unknown error_msg)