Algebra Help

One pair, because 17 is a prime number and 1+1=2 therefore a and b MUST be 17 because anything greater would yield a result less than 2/17. In addition, anything less than 17 wouldn't satisfy the equation because 17 is prime and 17 would be unobtainable as a LCD. Therefore the only pair would be (17,17). This yields the answer of only 1 pair.

Three positive pairs will satisfy the equation as follows:

 a = 9, b = 153
a = 153, b = 9
a = 17, b = 17