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 Infinite Triplet and Perfect Square (Posted on 2015-08-16)
Does there exist an infinite number of positive integer triplets (x,y,z) with x < y < z such that:
x, y and z describe an arithmetic sequence, and:
Each of xy+1, yz+1 and zx+1 is a perfect square?

 No Solution Yet Submitted by K Sengupta Rating: 3.0000 (1 votes)

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 a few more | Comment 2 of 3 |
Starting with Jer's three solutions, I note that the z = 2y-x.
Also that x = previous y/2 and y = previous z*2

That makes the next few solutions of this form
`x       y       z1	8	154	30	5615	112	20956	418	780209	1560	2911780	5822	108642911	21728	4054510864	81090	15131640545	302632	564719151316	1129438	2107560564719	4215120	78655212107560	15731042 29354524`
I have generated these using Excel and checked using Excel that these are all valid solutions.  And the first column is OEIS A001353

Thanks for the start, Jer.

Edited on August 16, 2015, 4:11 pm
 Posted by Steve Herman on 2015-08-16 16:07:44

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