The number of ordered pairs a , b of positive integers such that 2 a - 1 b and 2 b - 1 a are both integers is

Step-by-step solution

For positive integers ' a ' and ' b ' the numbers 2 a - 1 b and 2 b - 1 a are integers if ' a ' and ' b ' and odd integers because ' 2 a - 1 ' and ' 2 b - 1 ' are odd integers. Now, let 2 a - 1 b = α and 2 b - 1 a = β , where α , β are integers. then 2 a - 1 = α b and 2 b - 1 = β a so 4 a - 2 = α β a + 1 ⇒   a = α + 2 4 - α β ∵ a is an integer, then 0 < α β < 4 ∴ Possible v