Lubin
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21,726
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 53m comment Show that $K_1K_2/k$ is Galoisienne if $K_1$ and $K_2$ are Galoisienne. Are you restricting to the finite case? 1d answered Is there a formula for the cosine of 1/5 of an angle? 1d comment Is there a formula for the cosine of 1/5 of an angle? I read your answer to say that Wolfram gave you (only) two explicit solutions for $t$ in the special cases where $C=\pm1$. For $C=1$ there should be five (counting multiplicity), coming from the fifth roots of unity. Total three, since two roots should be double. 1d comment Is there a formula for the cosine of 1/5 of an angle? But if $C=\cos x$, then $C=1$ means $x=2k\pi$, and the values of $\cos(2k\pi/5)$ are easily found, in spite of what Wolfram claims. If $C=-1$, you’re talking about $\cos((2k+1)\pi/5)$, equally easily found. Nov 28 comment Is it always possible to find a vector, result from the sum of 2 elements of 2 different subspaces, which is not in the union of them? Yes indeed, and I hope you’ve shown that for yourself by direct computation. Nov 28 revised Determine all of the monic irreducible polynomials in $\mathbb Z_3 [x]$ of degree $4.$ clarification Nov 28 answered Determine all of the monic irreducible polynomials in $\mathbb Z_3 [x]$ of degree $4.$ Nov 27 comment How to factor $a^n - b^n$? This seems to me to be the best explanation of that factorization. I would have said that calling in the formula for a finite geometric series was overkill. Nov 27 awarded Great Answer Nov 26 answered Rational numbers from irrational numbers Nov 26 comment Rational numbers from irrational numbers @YvesDaoust, what you say is ambiguous (in English!). Better to say, “Every algebraic number evaluates to $0$ for some polynomial function”. Nov 26 comment Can every polynomial be represented as a field norm? Have you gotten any positive results beyond the case $n=1$? You should give us some idea what you’ve tried and maybe what’s gone wrong. Nov 25 revised Find a spherical triangle with angle sum $5π/3$ Corrected the title with the appropriate mathJax Nov 25 answered How does aptitude at solving Olympiad problems relate to success at further mathematical studies? Nov 25 comment Ring Isomorphism :$\Bbb{Z}[i]/\langle p\rangle\simeq \Bbb{Z}[x]/\langle x^2+1,p\rangle$ Your analysis of the situation in #2 is not correct. After all, $X^2+1$ is certainly in the kernel, isn’t it? So the kernel is definitely larger than $\Bbb Z[X]\cap (p)$. Nov 25 answered How do you obtain the sum in base 5 notation: Nov 25 comment Non-solvable polynomial over a PID $1$ and $-1$ are units, as is every power series with nonzero constant term, and therefore no prime divides either $1$ or $-1$. There is, for all intents and purposes, only one prime, namely $z$. You should make sure that you understand why a power series with nonzero constant term has a reciprocal in $\Bbb C[[z]]$. Nov 24 comment Problem with units in number field Thanks for the reference. It’s a really interesting note — you see that a huge fraction of the whole is devoted to finding the true basis of the units (modulo roots of unity). Nov 24 revised Is $\mathbb{Q}(\sqrt{5}, \alpha)$ over $\mathbb{Q}(\alpha)$, where $\alpha$ is the real seventh root of $5$ a the splitting field? supply ¿illuminating? example. Nov 24 answered Is $\mathbb{Q}(\sqrt{5}, \alpha)$ over $\mathbb{Q}(\alpha)$, where $\alpha$ is the real seventh root of $5$ a the splitting field?