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# HELP :(

+1
112
4
+91

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

mn−m+4n=40

Jun 23, 2022

#1
-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
+91
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it wrong :(

Derekshackk  Jun 23, 2022
#3
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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
+91
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help

Derekshackk  Jun 23, 2022