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Divide The Cubic, Get The Pairs (Posted on 2007-05-26) Difficulty: 3 of 5
Find all possible positive integers (p,q) with p≤q such that (q³+1)/(pq-1) is an integer.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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re: Solution (spoiler) | Comment 2 of 5 |
(In reply to Solution by Brian Smith)

I admire your analytical skill, Brian.  But there are only five solutions (p, q) = (1,2), (1,3) (2,2), (2,5) and (3,5).  Note that the given for the problem is that p <= q.

Edited on May 27, 2007, 4:55 pm
  Posted by Dej Mar on 2007-05-27 02:25:59

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