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How many perfect squares (Posted on 2006-04-25) Difficulty: 3 of 5
Suppose a and b are positive integers. We all know that aČ+2ab+bČ is a perfect square. Give an example where also aČ+ab+bČ is a perfect square. How many such examples exist?

See The Solution Submitted by Salil    
Rating: 3.0000 (2 votes)

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re: Partial Solution | Comment 2 of 19 |
(In reply to Partial Solution by tomarken)

As exemplified by (3,5), (6,10), (9,15),(12,20), any integral multiple of one solution is another solution, so each such family of a given ratio has infinitely many members.
  Posted by Charlie on 2006-04-25 09:54:50

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