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Square Result Rumination (Posted on 2014-09-28) Difficulty: 3 of 5
Each of X and Y is a positive integer such that each of X+Y and X/Y is a perfect square.

Does there exist an infinite number of pairs (X,Y) satisfying all the given conditions?
Give reasons for your answer.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts re: other types of cases Comment 6 of 6 |
(In reply to other types of cases by Charlie)

Exactly. y=b^2+1 is simply an obvious substitution. More precisely, y=a^2/(b^2+1), giving many additional possibilities:


a=2n, b=1, x=y=2n^2  
a=5n, b=2, x=5(2n)^2, y=5n^2  
a=10n, b=7, x=2(7n)^2, y=2n^2

etc.

In fact it seems that there are infinitely many solutions for every possible value of b in N.


Edited on September 29, 2014, 3:06 am
  Posted by broll on 2014-09-29 02:58:24

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