There are 13 solutions for which b<=8 because the equation can be rearranged to solve for k: k = (a-b)(b/a)
For b to be less than or equal to 8, a can be any positive integer greater than 8 and b can be any positive integer from 1 to 8. Therefore, when a is fixed, there are 8 possible values for b and when b is fixed, there are a-b possible values for k. This gives a total of 8*(a-b) = 8*(a-8) = 8a-64 solutions. As a must be greater than 8, the total number of solutions is 13 (8+9+10+11+12+13+14+15+16 = 13*8 = 104 = 8a-64).