Question

Find the number of pairs (a,b) of integers such that
a+2/a+5=b/3

Answer 1

6

Explanation:

The expression can be rearranged to ...

b = 3 -9/(a+5)

In order for b to be an integer, (a+5) must be an integer divisor of 9. There are exactly 6 of those: ±1, ±3, ±9.

The attached table shows the values (a, b) = (x₁, f(x₁)).