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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(3): Partial Solution | Comment 5 of 19 |
(In reply to re(2): Partial Solution by tomarken)

The formula does seem to work.  I haven't worked out how it works however; I'd like to see the derivation or proof.

The formula does not, however, provide all the base pairs. While it provides (7,8), it does not provide (7,33). It doesn't provide those base pairs where neither member is prime, such as (16,39) or (65,88).

But it does show there are infinitely many base pairs.

  Posted by Charlie on 2006-04-25 11:03:53
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