# $n$ integers, $a_i a_j +1$ all perfect squares [closed]

Find all numbers $n$ so that there exists $n$ integers $a_1, a_2, ..., a_n$: $a_i \ge 2$ and $a_i\cdot a_j +1 (\forall i\not = j)$ are all perfect squares.

## closed as off-topic by Martin R, Hippalectryon, user230715, Ofir Schnabel, David KNov 5 '15 at 13:43

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• Look up 0,1,3,8,120 in the Online Encyclopedia of Integer Sequences (oeis.org) – Empy2 Nov 5 '15 at 12:18
• it's so useful. Thank you :D – toituhoc Nov 5 '15 at 12:36
• so what about $a_i\cdot a_j - 1$ are all perfect squares? – toituhoc Nov 5 '15 at 12:42
• You should also check A.Dujella's web page on Diophantine $m$-tuples. – Julián Aguirre Nov 5 '15 at 13:43
• there is an old IMO problem, with tuples 2, 5, 13, d. I generalized it last year. It's amazing to see the original unsolved problem :D – toituhoc Nov 6 '15 at 4:05