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.

If the problem allowed 0 there are an infinite number of solutions:
(0,a,2a) where a(1)=0, a(2)=12, a(n)=6*a(n-1)-a(n-2)

Including negatives also would allow (-1,0,1)

The only actual solutions I've found allowed by the problem:
(1,8,15)
(4,30,56)
(15,112,209)

I haven't been able to make much use of OEIS so far.

Posted by Jer on 2015-08-16 14:57:16