How many of the ordered pairs of positive integers (T, G) satisfy the equation: T + G + TG = 2018 ?
T + G + TG = 2018
i.e. 1 + T + G + TG = (T + 1)(G + 1) = 2019 = 3×673.
As T, G are positive integers, both the terms (T + 1) and (G + 1) are greater than or equal to 2. Also they are factors of 2019.
So required number of ordered pairs of positive integers (T, G) = (number of positive integral divisors of 2019) – 2 = 4-2 = 2 .