Difference between revisions of "Mock AIME 2 2006-2007 Problems/Problem 1"
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Revision as of 20:22, 15 September 2006
Problem
A positive integer is called a dragon if it can be written as the sum of four positive integers and
such that
Find the smallest dragon.
Solution
From we have that 16 divides
. From
we have
. Minimizing
minimizes
and
and consequently minimizes our dragon. The smallest possible choice is
, from which
and
so our desired number is
.