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Reciprocal Equation #5 (Posted on 2013-10-15) Difficulty: 3 of 5
Find all pairs (A, B) of 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.

No Solution Yet Submitted by K Sengupta    
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  Subject Author Date
SolutionRest of a solutionBrian Smith2016-07-04 09:45:19
Some ThoughtsPart of a solutionBrian Smith2016-07-03 21:01:30
Solutioncomputer generated answers without proofCharlie2013-10-15 12:41:22
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