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Generating triplets of squares (Posted on 2018-03-25) Difficulty: 4 of 5
Find infinitely many triples (a,b,c) of distinct positive integers such that a, b, c are in arithmetic progression and ab+1,bc+1,ca+1 are perfect squares.

No Solution Yet Submitted by Ady TZIDON    
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re: a partial list of infinity | Comment 3 of 5 |
(In reply to a partial list of infinity by Dej Mar)

It's not possible to list them all, of course, but there is a formula that generates the members of your list.

The recurrence for each triple (a(n),b(n),c(n)) can be written as
a(n)=4*a(n-1)-a(n-2) 
b(n)=2*a(n+1)
c(n)=a(n+2)
but I don't have proof of this yet.  (Nor do I have proof that there aren't others not covered here.)

  Posted by Jer on 2018-03-26 09:52:43
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