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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(4): Partial Solution | Comment 6 of 19 |
(In reply to re(3): Partial Solution by Charlie)

Yeah, I noticed that there were some pairs you had come up with (like 7 and 33) that wouldn't be found by my formula.  I'm not sure if there is an alternate way to find those other pairs, I didn't immediately recognize a pattern...

I'll see if I can come up with some kind of proof for why the formula I came up with works, although that's not really my area of expertise. :)

  Posted by tomarken on 2006-04-25 11:08:12
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