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If a, b, and c are positive integers satisfying ab+c = bc+a = ac+b = 2, what is the value of a+b+c?

 Jun 24, 2022
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Take \(ab + c = 2\). From the first words, we know that c must be 1, because if c was 2, \(ab = 0\), which is not possible with positive integers. 

 

This means \(c = 1 \), and \(ab = 1\)

 

The only positive integers that satisfy this are: \(a = b = c = 1 \)

 

Thus, \(a + b + c = \color{brown}\boxed{3}\)

 Jun 24, 2022

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