Mock AIME 3 2006-2007 Problems/Problem 4
Problem
Let 
where 
. If 
and 
are positive integers such that 
is an integer, then find the minimum value of 
Solution
Pairing the terms 
with 
for 
all result in integers, so we're left with making 
an integer.
. To make this an integer, we just multiply it by its conjugate 
, so 
