*distinct nonzero integers*with A ≠ -1 and B ≠ -1 such that (1 + 1/A) is a

*nonzero integer multiple*of (1 + 1/B).

Prove that there are no others.

__Note__: (1 + 1/A) is can be a negative as well as positive integer multiple of (1 + 1/B). So, equations like: (1 + 1/A) = -2(1 + 1/B) or, (1 + 1/A) = (1 + 1/B) are permissible. Remember, A and B

*must be distinct*.