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?

Give reasons for your answer.

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 z

1 8 15

4 30 56

15 112 209

56 418 780

209 1560 2911

780 5822 10864

2911 21728 40545

10864 81090 151316

40545 302632 564719

151316 1129438 2107560

564719 4215120 7865521

2107560 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**