+343 How many pairs of positive integers \((a,b)\) satisfy \(\frac{1}{a} + \frac{1}{b}=\frac{2}{17}\)?
+4622 1/a + 1/b = 2/17
b/ab+a/ab=2/17
a+b/ab=2/17
17(a+b)=2ab
17a+17b=2ab
2ab-17a-17b=0
Multiply the equation by two...
4ab-34a-34b=0
If 289(17^2) is added to both sides, then (2a-17)(2b-17)=289.
289=1*289 and 17*17.
2a-17=1
2a=18 a=9 2b-17=289 2b=153 (9,153), (153,9)
2a-17=17 2a=34 a=17 2b-17=17, 2b=34, b=17 (17,17)
Thus, there should be three(3) positive ordered pairs.
