How many pairs of positive integers (a,b) satisfy 1/a + 1/b = 2/17 ?

Thanks in advance!

Guest Feb 9, 2019

#1**0 **

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.

vindou Feb 9, 2019