+91 Find the number of pairs of integers (m,n) that satisfy the equation:
mn−m+4n=40
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 \(\boxed{9}\)
+2668 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?
