perplexus.info :: Just Math : Diophantine Pair Decision

Diophantine Pair Decision (Posted on 2016-08-13)

Each of X and Y is a distinct positive integer, such that:

X and Y are relatively prime, and:
Each of (X² – 12)/Y and (Y²– 12)/X is an integer.

Does there exist an infinite numbers of pairs (X,Y) satisfying the given conditions?

Give reasons for your answer.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Yes! There exist an infinite numbers of pairs (X,Y) satisfying the given conditions.
For an explanation, refer to the solution submitted by broll in this location.

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

Subject	Author	Date
Possible solution	broll	2016-08-14 05:01:27
OEIS to save the day!	Brian Smith	2016-08-13 21:44:57
Dead Ends?	Steve Herman	2016-08-13 20:03:47

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