Find the number of ordered pairs $(a,b)$ of integers such that \frac{a + 2}{a + 1} = \frac{b}{12}.
(a+ 2) / (a + 1) = b/12
Rearrange as
12 ( a + 2) / ( a + 1) = b
This will converge to ≈ 12 as a becomes more positive and more negative
a b
0 24
1 18
2 16
3 15
5 14
11 13
-2 0
-3 6
-4 8
-5 9
-7 10
-13 11