David75
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# 38 Actions

 Jul2 awarded Curious Oct22 accepted Ring of $p$-adic integers $\mathbb Z_p$ Oct22 accepted Discrete valuation on $p$-adic numbers Oct21 awarded Editor Oct21 revised Discrete valuation on $p$-adic numbers added 18 characters in body Oct21 comment Discrete valuation on $p$-adic numbers Yes, of course. Sorry, I forgot, that $\mu_n(w)=v.$ Oct21 asked Discrete valuation on $p$-adic numbers Oct15 asked Ring of $p$-adic integers $\mathbb Z_p$ Dec2 comment Proving equation (with Hilbert symbol) Thanks! It's clear now :-) Dec2 comment Proving equation (with Hilbert symbol) I've computed: $(-ab,-c)=(-c,a)(-c,-b)=(-1,ac)(-c,-b)=(-1,ac)(-c,b)(-c,-1)=(-1,ac)(-1,bc)(-1,-c‌​)=(-1,-acbcc)$. But where is a mistake? Dec2 asked Proving equation (with Hilbert symbol) Apr23 accepted Existence of irreducible polynomials Apr22 comment Existence of irreducible polynomials Ok, but it is not clear, that $f$ has only real roots. Maybe my question was a bit vague. All roots of the polynomial $f$ should be elements in $\mathbb R$. Apr22 awarded Commentator Apr22 comment Existence of irreducible polynomials Good idea. It would be great, if you have a source or a proof for it. Apr22 comment Existence of irreducible polynomials Thanks for your answer. Apr22 asked Existence of irreducible polynomials Mar30 comment Realizing $S_n$ as a Galois group You're right. There must exist a transposition, a $n-1$-cycle and the galois group have to be a transitive subgroup of $S_n$. Then the galois group is $S_n$. But I can't see, why a $n-1$-cycle exists. Mar30 asked Realizing $S_n$ as a Galois group Jan17 accepted Proof of inequality (mollifier)