+0  
 
+1
60
4
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Find the number of ordered pairs (m,n) of integers that satisfy \(mn = 2m + 4n. \)
 

 Mar 31, 2020
 #1
avatar+111321 
+2

 

mn  =  2m  + 4n        rearrange  as

 

mn - 4n =  2m

 

n ( m - 4)  =  2m

 

n  =    2m  / [ m  - 4 ]

 

When

   m          n

   0            0

   3            -6

   5           10

   6            6

   8            4

  12           3

    2          -2

   -4           1

 

cool cool cool

 Mar 31, 2020
edited by CPhill  Mar 31, 2020
edited by CPhill  Mar 31, 2020
 #2
avatar
+2

So it's 8? Tysm!

Guest Mar 31, 2020
 #3
avatar+4569 
+1

Another way:

 

Rearrange the equation mn=2m+4n as mn-2m-4n=0

 

Notice that this equation is close to (m-4) * (n-2) is eight is added to both sides.

 

(m-4) * (n-2) = 8

 

8=2^3, so four factors.

 

2(4)=8-total ordered pairs(negative and non-negative)......

 Mar 31, 2020
edited by tertre  Mar 31, 2020
 #4
avatar+111321 
0

Thx, tertre  !!!!

 

 

cool cool cool

CPhill  Mar 31, 2020

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