How many pairs of positive integers (a,b) satisfy 1/a+1/b=2/17?
2/17 = 1/a + 1/b
Assuming that a, b are different integers
We can use something known as "Egyptian Fractions" here
Divide 17/2 = 8.5 .....take the next greatest integer = 9 and write 1 over this = 1/9
Subtract this from 2/17
2/17 - 1/9 = 1/153
So
1/9 + 1/153 = 2/17
So { a, b} = ( 9, 153} or {153, 9 }