query: Why is it that $\exists f_1,f_2\in M[f_1, f_2$ have no common factor]?
positive_passages.docid: 141687
positive_passages.text: Nonprincipal prime ideals contain two relatively prime elements
negative_passages.docid: 106401
negative_passages.text: Prove: $p-mq | f(m)$ where $m$ is any integer
negative_passages.docid: 91947
negative_passages.text: Proof of $ f:I_n \rightarrow I_m \Rightarrow n = m$
negative_passages.docid: 120940
negative_passages.text: An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
negative_passages.docid: 97024
negative_passages.text: If $F/k$ normal, $g,h \in F[X]$ monic irreducible factors of $f \in k[X]$, then $\exists\ \sigma \in Aut(F/k)$ s.t. $g^\sigma = h$.
negative_passages.docid: 74224
negative_passages.text: On irreducible factors of $x^{2^n}+x+1$ in $\mathbb Z_2[x]$
negative_passages.docid: 75863
negative_passages.text: how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
negative_passages.docid: 61640
negative_passages.text: Prove c exists for f:[0,1] -> R
negative_passages.docid: 141683
negative_passages.text: $ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$
negative_passages.docid: 135606
negative_passages.text: No function $f:\mathbb{Z}\rightarrow \{1, 2, 3\}$ satisfying $f(x)\ne f(y)$ for all integers $x,y$ and $|x-y|\in\{2, 3, 5\}$
negative_passages.docid: 93686
negative_passages.text: In a UFD, lcm = product for coprimes: $\,(a,b)=1,\ a,b\mid c\Rightarrow ab\mid c$
negative_passages.docid: 100001
negative_passages.text: Show that a continuous function doesn't exist such that for every real $c$, there exist exactly two reals $a, b$ s.t. $f(a)=f(b)=c$.
negative_passages.docid: 75970
negative_passages.text: $\mathbb Z[1/2]$ is not finitely generated?
negative_passages.docid: 112807
negative_passages.text: Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective
negative_passages.docid: 62504
negative_passages.text: Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$
negative_passages.docid: 95299
negative_passages.text: What can you say about $f$ and $g$ in the case that $fg$ is 1) Injective, 2) Surjective - Cohn - Classic Algebra Page 15
negative_passages.docid: 119256
negative_passages.text: Function $f\in M[G]$, $f:\kappa\to M$ is in the ground model implies $\kappa^+$-Baire