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(n1)a(n2)
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 20150816 14:57:16 