query: Fields: Prove $1+1=0$
positive_passages.docid: 16384
positive_passages.text: Proving a result in a given field
negative_passages.docid: 96894
negative_passages.text: Prove $f_{n+1}^2+f_n^2=f_{2n+1}$
negative_passages.docid: 61782
negative_passages.text: How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
negative_passages.docid: 91622
negative_passages.text: Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
negative_passages.docid: 59006
negative_passages.text: Proof of $\gcd(n!+1, (n+1)!+1)=1$?
negative_passages.docid: 105164
negative_passages.text: If $abc=1$, prove that $\frac{2}{(a+1)^2+b^2+1} + \frac{2}{(b+1)^2+c^2+1} + \frac{2}{(c+1)^2+a^2+1} \le 1$.
negative_passages.docid: 142530
negative_passages.text: Let K be a field, and $I=(XY,(X-Y)Z)⊆K[X,Y,Z]$. Prove that $√I=(XY,XZ,YZ)$.
negative_passages.docid: 57981
negative_passages.text: Alternative proof of $a\times0= 0$
negative_passages.docid: 44161
negative_passages.text: Using induction to prove $\sum_{k=0}^{N-1} 2^k = 2^N-1$
negative_passages.docid: 70776
negative_passages.text: Characteristic of a field is $0$ or prime
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 25775
negative_passages.text: How to prove $(1+1/x)^x$ is increasing when $x>0$?
negative_passages.docid: 100571
negative_passages.text: Prove $(1-a)(1-b)(1-c)(1-d)\geq abcd$ if $a^2+b^2+c^2+d^2=1$
negative_passages.docid: 31783
negative_passages.text: Is this proof of $ab = 0$ correct?
negative_passages.docid: 102464
negative_passages.text: Prove $R < ( 1 + (\sum |a_{i}|^{p} )^{q/p})^{1/q}$ for absolute value of polynomial zeros
negative_passages.docid: 95057
negative_passages.text: Possible fake proof of $1= -1$
negative_passages.docid: 99052
negative_passages.text: Prove that $( 1 + n^{-2}) ^n \to 1$.