We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+2
208
2
avatar+164 

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

 Apr 10, 2018
 #1
avatar+100588 
+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

 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

 Apr 10, 2018

12 Online Users

avatar
avatar