Find all possible pairs of positive integers (x,y) such that both x²+5y and y²+5x are perfect squares.

I would like to congratulate Charlie and Eric for their solution of this problem by their respective  methodologies which are precise and accurate in all respects. 
       While on the subject, I would also like to acknowledge the various posts  of e.g. in this respect  who made a very nice effort at solving a complex problem at the outset, without the benefit of any hint/tips. 

 

Posted by K Sengupta on 2006-06-26 03:31:10