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Integer Pair and Prime Constant (Posted on 2009-10-24) Difficulty: 3 of 5
Determine all possible value(s) of a positive prime constant P such that the equation: 2X 3P = Y2 has precisely two distinct solutions in (X, Y), where each of X and Y is a positive integer.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Intuition | Comment 1 of 3
From what I can tell so far, 5 is the only value of P for which there are exactly 2 solutions, which are (X,Y) = (4,1) and (6,7).  I don't think any solutions are possible for P=2, and there may be only one solution for all remaining P.
  Posted by Jim Keneipp on 2009-10-24 15:39:29
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