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

Creeperhissboom  Apr 10, 2018
 #1
avatar+92367 
+2

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 }

 

 

cool cool cool

CPhill  Apr 10, 2018
 #2
avatar
0

a = -136, b = 8

a = 8, b = -136

a = 9, b = 153

a = 17, b = 17

a = 153, b = 9

Guest Apr 10, 2018

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