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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 9 of 19 |
(In reply to re(3): Partial Solution by Charlie)

I cannot provide any derivation of proof, but here is a formula, modified from the one provided by tomarken, that will provide for the pair (7,33) and many others:

if a is a prime number,

b = ((a-1)/2)2 + (a2-1)/2

 

Edited on April 25, 2006, 12:35 pm
  Posted by Dej Mar on 2006-04-25 12:26:43

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