Y by
Let
be an integer. Find all tuples of real numbers
such that
is a permutation of
.


![\[
2a_1 - 3a_2,\ 2a_2 - 3a_3,\ \ldots,\ 2a_n - 3a_1
\]](http://latex.artofproblemsolving.com/c/0/9/c098bda64393b12049d319db49815947b2a0b7a4.png)

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\[ \left((x^2+1)+(\sqrt{2}x+\sqrt{2})\right)\left((x^2+1)-(\sqrt{2}x+\sqrt2})\right)= 0 \]
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