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

 

 

 

Thanks in advance!

 Feb 9, 2019
 #1
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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.

 Feb 9, 2019
 #2
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Thank you, but that answer is incorrect.

Guest Feb 9, 2019
 #3
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Three positive pairs will satisfy the equation as follows:

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

 Feb 9, 2019

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