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

As Charlie pointed out, the solutions can go on infinitely as long as they are integral multiples of one of the "base pairs".  Here is the formula to find the base pairs, which themselves appear to go on infinitely:

Let a = any prime number greater than or equal to 5.

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

As long as you choose a prime number for a, you can find the value for b that will make a^2 + ab + b^2 = a perfect square.

 Posted by tomarken on 2006-04-25 10:08:34 Please log in:

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