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 K Nov 5 '15 at 13:43

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  • $\begingroup$ Look up 0,1,3,8,120 in the Online Encyclopedia of Integer Sequences (oeis.org) $\endgroup$ – Empy2 Nov 5 '15 at 12:18
  • $\begingroup$ it's so useful. Thank you :D $\endgroup$ – toituhoc Nov 5 '15 at 12:36
  • $\begingroup$ so what about $a_i\cdot a_j - 1$ are all perfect squares? $\endgroup$ – toituhoc Nov 5 '15 at 12:42
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    $\begingroup$ You should also check A.Dujella's web page on Diophantine $m$-tuples. $\endgroup$ – Julián Aguirre Nov 5 '15 at 13:43
  • $\begingroup$ 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 $\endgroup$ – toituhoc Nov 6 '15 at 4:05