query: Quartic Formula existance
positive_passages.docid: 19073
positive_passages.text: Is there a general formula for solving 4th degree equations (quartic)?
negative_passages.docid: 26698
negative_passages.text: Math beyond Quaternions
negative_passages.docid: 93820
negative_passages.text: Fermat's little theorem applied for $n$'th root existence $\!\bmod p$
negative_passages.docid: 103763
negative_passages.text: Minimal polynomial of $\sqrt{2}+\sqrt{3}$ over $\mathbb Q$
negative_passages.docid: 84017
negative_passages.text: Is $\sqrt[3]{2}$ contained in $\mathbb{Q}(\zeta_n)$?
negative_passages.docid: 148876
negative_passages.text: What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
negative_passages.docid: 115583
negative_passages.text: prove that $a^2(p-q)(p-r)+b^2(q-p)(q-r)+c^2(r-p)(r-q)\ge 0$
negative_passages.docid: 47001
negative_passages.text: Cubic diophantine equation
negative_passages.docid: 10111
negative_passages.text: Prove or disprove that Q[√2] is a field
negative_passages.docid: 147952
negative_passages.text: Why can we prove mathematically that a formula to solve an (n+5) order polynomial does not exist?
negative_passages.docid: 15436
negative_passages.text: Find p and q s.t. $({p-1})^{q-1}+({q-1})^{p-1} \equiv 101 \pmod {pq}$
negative_passages.docid: 30480
negative_passages.text: Continued product in $\sin$ series
negative_passages.docid: 17786
negative_passages.text: Existence of Consecutive Quadratic residues
negative_passages.docid: 149661
negative_passages.text: For $n=pq$, show that there exist $\alpha, \beta \in Z_n^*$ such that $\alpha, \beta \notin (Z_n^*)^2$ and $\alpha \cdot \beta \notin (Z_n^*)^2$.
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 56928
negative_passages.text: $\dfrac{pq}{r}+\dfrac{qr}{p}+\dfrac{pr}{q}\in\Bbb Z\,\Rightarrow\, \dfrac{pq}{r},\dfrac{qr}{p},\dfrac{pr}{q}\in\Bbb Z$
negative_passages.docid: 122932
negative_passages.text: When $(\mathbb{Q}(\zeta_n) : \mathbb{Q}) = 2$?