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

Guest Jun 24, 2022

#1**0 **

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

BuilderBoi Jun 24, 2022