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How many distinct ordered pairs of positive integers (m,n) are there so that the sum of the reciprocals of m and n is 1/4?

 Jan 15, 2020
 #1
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Let z   =  4

Let  m  = z + a

Let n  = z + b

 

And  we  can    find  a, b    such that

 

ab   =  z^2

 

ab   = 4^2

 

ab  = 16

 

The factors of 16 are

 

1  2  4  8   16

 

So

a   b

1  16

2    8

4    4

 

So

m      n

5      20       accept

6      12       accept

8       8        reject    since  m,n  are distinct   

 

 

cool cool cool

 Jan 15, 2020

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