Mock AIME 3 2006-2007 Problems/Problem 2
Revision as of 00:25, 30 December 2009 by Darkprince (talk | contribs) (Created page with '== Problem == If <math>abc - ab - bc - ca + a + b + c = 2008</math> for positive integers <math>a</math>, <math>b</math>,and <math>c</math>,then determine the minimum value of <m…')
Problem
If 
for positive integers 
, 
,and 
,then determine the minimum value of 
.
Solution
Subtract 1 from both sides to make 
. From factorization, let 
. Any other prime factorization would increase one of three to be much greater than 224, so this minimizes the sum of 
.
