Mock AIME 4 2006-2007 Problems/Problem 9
From AoPSWiki
Problem
Compute the smallest positive integer
such that the fraction 
Solution
Suppose 
is a common divisor of 
and 
. Then 
also divides 
for integers 
. Putting 
and 
gives 
. Since 
is prime and , we have 
. Thus divides , or 
or 
. Since we are looking for the smallest positive solution, our answer is 
.
