 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  How many perfect squares (Posted on 2006-04-25) Suppose a and b are positive integers. We all know that a˛+2ab+b˛ is a perfect square. Give an example where also a˛+ab+b˛ is a perfect square. How many such examples exist?

 See The Solution Submitted by Salil Rating: 3.0000 (2 votes) Comments: ( Back to comment list | You must be logged in to post comments.) re(2): Complete Solution | Comment 17 of 19 | (In reply to re: Complete Solution by Salil)

An inadvertent omission had occurred in my post giving the complete solution to the problem under reference.

While the given formula a= K(x + y)(x-3y) and b = 4Kxy does generate the desired pairs (a,b) corresponding to positive integers  x and y; the magnitude of K is POSITIVE RATIONAL NUMBER AND THEREFORE WOULD ALSO BE INCLUSIVE OF INTEGRAL VALUES. I would shortly be amending the texts constituting my original post.

Regarding your query, it would be observed that substituting

x=5; y=1 and K = 1/4 will yield the  desired pair (a,b) = (3,5)

 Posted by K Sengupta on 2006-04-28 10:42:23 Please log in:

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