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 Square Result Rumination (Posted on 2014-09-28)
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 No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 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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