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Ratio Sum Equals Positive Integer (Posted on 2015-08-30) Difficulty: 3 of 5
Does there exist an infinite number of positive integer pairs (x, y) such that:
(x+1)/y + (y+1)/x is a positive integer?

Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
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re(2): Answer, maybe full solution. Comment 3 of 3 |
(In reply to re: Answer, maybe full solution. by Steve Herman)

The answer to the question is Yes.

It appears the only integers that can appear as the sum are 3 and 4.
There are an infinite number of solutions for each.

(2,2) gives 3
(1,1) gives 4

(y,y(y+1)/x) gives the same number as (x,y) so you can use this to generate an infinite number of solutions from each starting point.

  Posted by Jer on 2015-08-30 20:54:31

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