How to find the roots of $x^4 +1$ - Mathematics Stack Exchange
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Factor $x^4+1$ over $\\mathbb{R}$ - Mathematics Stack Exchange
In complicated terms, the field extension $\mathbb C / \mathbb R$ has degree $2$, so you expect every quartic to be reducible over $\mathbb R$.
Find the splitting field of $x^4+1$ over $\\mathbb Q$.
2017年8月11日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Compute integral $\\int_{-\\infty}^\\infty \\frac{x^4}{1+x^8} \\, dx$
Compute the integral. $$\int_{-\infty}^\infty \frac{x^4}{1+x^8} \, dx$$ The answer at the back of the book is $$\frac{\pi}{4\sin(\frac{3\pi}{8})}$$
polynomials - Show that $x^4 +1$ is reducible over $\mathbb {Z}_ …
An abstract algebra argument, without much computation. Claim: The polynomial $x^4+1$ splits over $\mathbb F_{p^2}$ for any odd (*) prime $p$.
Proving that $X^4+1$ is reducible over all finite prime fields
I think the proof based on $8|p^2-1$ is the simplest proof. Here is another one: In the algebraic closure $\overline{\mathbb F_p}$ we have the decomposition
How can I systematically find the roots of $ x^4 + 1?$ Is there …
Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Why is $X^4+1$ reducible over $\\mathbb F_p$ with $p \\geq 3,
over any field, all the roots of the right hand side are contained in $\;\Bbb F_{p^2}^*\;$ , and since this is an extension of degree two over the prime field $\,\Bbb F_p\,$ (and observe that $\,x^4+1\,$ is always a polynomial over this prime field!), it cannot be this polynomial is irreducible over the prime field since then any of its roots ...
abstract algebra - Prove or disprove that $X^4+1$ is irreducible in ...
2017年12月22日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Show that $x^4+1$ is reducible in $\\Bbb Z_p$ for every prime $p ...
2017年9月30日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.