Answer:
4
Explanation:
The left side of the equation can be factored as the difference of squares:
(a -b)(a +b) = 105
The right side of the equation can be factored to 4 different pairs of factors:
105 = 1·105 = 3·35 = 5·21 = 7·15
For each of the factor pairs, we can match factors to get, for example, ...
a -b = 1
a +b = 105
The solution to this is a = (105 +1)/2 = 53, b = (105 -1)/2 = 52. Thus, we have ...
(a, b) = (53, 52)
For the other factor pairs, the solutions are ...
(a, b) = (19, 16), (13, 8), (11, 4)
There are a total of 4 positive integer solutions.