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Is there a polynomial with coefficients -1,0,1 which is irreducible over the rationals and has the alternating group as its galois group ?

More concrete : Is there a polynomial of degree n, all coefficients -1,0 or 1, irreducible over the rationals with galois group A(n) ?

For small degrees, I enumerated the polynomials and none had the property. So I am curious if there are really none.

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    $\begingroup$ It may take a while to fond one. Think of the almost, but not totally unrelated fact the the cyclotomic polynomials $\Phi_n$ have coefficients in $\{-1,0,1\}$ until you check $n=105$. $\endgroup$ – Hagen von Eitzen May 29 '13 at 21:39
  • $\begingroup$ There might be some clues in math.stackexchange.com/questions/286944/… $\endgroup$ – Mark Bennet May 29 '13 at 21:44
  • $\begingroup$ I checked the polynomials up to degree 8 and there is none. $\endgroup$ – user81078 Jun 5 '13 at 14:46
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x^9 - x^8 - x^7 - x^6 + x^5 + x^4 + x^3 + x - 1

is a polynomial with Galois-Group A(9)

as I calculated with MAGMA online.

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    $\begingroup$ Hi Peter, it looks like you have multiple accounts on this website. I would suggest registering one of your accounts and follow the steps described here to consolidate your various accounts. $\endgroup$ – Willie Wong Jun 5 '13 at 15:31
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    $\begingroup$ would you mind giving some explanation of how you derived this? $\endgroup$ – robjohn Jun 5 '13 at 15:41

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