+0  
 
+1
35
4
avatar+82 

Find the  number of pairs of integers (m,n) that satisfy the equation:
                                   

                                        mn−m+4n=40

 
 Jun 23, 2022
 #1
avatar
-1

We can "finish the square" except this time it's not a square. We can factor the left side into (m+4)(n-1)+4, and subtract 4 from both sides: (m+4)(n-1)=36. Now 36 has 9 factors(2^2*3^2, so (2+1)(2+1)=9),so there are 9 pairs of numbers whos product is 36. So the answer is \(\boxed{9}\)

 
 Jun 23, 2022
 #2
avatar+82 
0

it wrong :(

 
Derekshackk  Jun 23, 2022
 #3
avatar+1746 
+2

The equation factors to: \((m+4)(n-1) = 36\)

 

Now, recall the factor of 36: 1,2,3,4,6,9,12,18,36

 

We need to find the number of pairs of integers that satisfy this. 

 

For example, 1 pair is \((32,2)\), because 36 x 1 = 36. 

 

Can you take it from here?

 
 Jun 23, 2022
 #4
avatar+82 
+1

help

 
Derekshackk  Jun 23, 2022

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