If a, b, and c are positive integers satisfying ab + c = bc + a = ac + b = 2, what is the value of a + b + c?
ab + c = 2
bc + a = 2
ac + b = 2
ab + c = ac + b ab + c = bc + a
ab - ac = b - c ab - bc = a - c
a ( b - c) = b - c b ( a - c) = a - c
a = ( b - c) / ( b - c) b = ( a - c) / (a - c)
a = 1 b = 1
So c also = 1
So
a + b + c = 3
