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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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Solution re(5): Partial Solution | Comment 8 of 19 |
(In reply to re(4): Partial Solution by Charlie)

Thanks for the list, Charlie!

It now seems that for all the prime numbers, a second value of b can be found:

b = a^2 - ((a+1)/2)^2

 


  Posted by tomarken on 2006-04-25 11:40:02
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