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Infinitely Diophantine (
Posted on 20160610
)
Each of X, Y and Z is a positive integer > 1 such that:
(X
^{2}
+ 1) (Y
^{2}
+ 1) = (Z
^{2}
+ 1)
Does there exist an infinite number of solutions to the above equation?
Give reasons for your answer.
No Solution Yet
Submitted by
K Sengupta
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Comment 2 of 2 
From the equation comes
(xy)^2 + x^2 + y^2 = z^2
(xy)^2 + n^2 + 2nxy is a square for each value of n
Then when y=2x^2 or x=2y^2 z^2 will be square
For ex x=7 2x^2=98 Then if y=98, z will be square. For ex y=98
(7^2+1)(98^2+1)=693^2+1
Edited on
June 11, 2016, 12:52 pm
Posted by
armando
on 20160611 11:04:10
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