Mock AIME 3 2006-2007 Problems/Problem 2
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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 
.
