Small Sum of Set Members

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Let set S S be the set of distinct positive integers that can be represented in the form 6 x + 96 y 6x+96y , where x , y Z x, y \in \mathbb{Z} . Find the minimum value of the sum of 2 distinct elements in S S .


The answer is 18.

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1 solution

Ben Frankel
Dec 16, 2013

gcd ( 6 , 96 ) = 6 \gcd(6, 96) = 6 , so S S is simply the set of positive multiples of 6. The smallest sum of 2 distinct elements is thus 6 + 12 = 18 6 + 12 = \fbox{18} .

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