perplexus.info :: Just Math : Infinitely Diophantine

Infinitely Diophantine (Posted on 2016-06-10)

Each of X, Y and Z is a positive integer > 1 such that:

(X² + 1) (Y² + 1) = (Z² + 1)

Does there exist an infinite number of solutions to the above equation?
Give reasons for your answer.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

(i) broll has provided two parametric solutions in this location..
(ii) armando has provided a parametric solution in this location..
Each of these parametric solutions proves beyond doubt that there are indeed an infinite number of solutions to the given equation.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	armando	2016-06-11 11:04:10
Two solutions	broll	2016-06-10 08:02:21

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