Q13/022) How many ordered pairs of integers (a,b) are there such that 1/a+1/b=1/200?

1/a+ 1/b= 1/200

or 200 b + 200 a = ab

or ab - 200 a - 200 b = 0
or (a-200) (b-200) = 40000 = 5^4 * 2 ^ 6
it has got (4+1) * (6+1) or 35 ordered solution for (a b) and 35 for (b a) so 70 solutions as 40000 can be factored in 35 ways( positive solutions)