query: How to factor $x-y$ out of $x^n - y^n$ for some arbitrary $n\in \mathbb{N}$
positive_passages.docid: 87665
positive_passages.text: Proving $x^n - y^n = (x-y)(x^{n-1} + x^{n-2} y + ... + x y^{n-2} + y^{n-1})$
negative_passages.docid: 15268
negative_passages.text: Find all $x,y \in \mathbb N^*$ such that $\frac{1}{x} + \frac{1}{y}=5$
negative_passages.docid: 42883
negative_passages.text: Cross product in $\mathbb R^n$
negative_passages.docid: 104602
negative_passages.text: asymptotic of $x^{x^x} = n$
negative_passages.docid: 24626
negative_passages.text: Irreducibility of $X^n - 2$ over $\mathbf Z[i]$.
negative_passages.docid: 116361
negative_passages.text: Relationship between prime factorizations of $n$ and $n+1$?
negative_passages.docid: 2043
negative_passages.text: $X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
negative_passages.docid: 30167
negative_passages.text: Convergence of $\sqrt[n]{x^n+y^n}$ (for $x, y > 0$)
negative_passages.docid: 53725
negative_passages.text: Factor $(x+y)^4+x^4+y^4$
negative_passages.docid: 97654
negative_passages.text: Rewrite a real polynomial in real (but only linear and quadratic) factors
negative_passages.docid: 136933
negative_passages.text: Which $n$ can be expressed as $x^2 − y^2$?
negative_passages.docid: 72500
negative_passages.text: Python factorization
negative_passages.docid: 10589
negative_passages.text: How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
negative_passages.docid: 67026
negative_passages.text: Best way to find all factors of a given number
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 2944
negative_passages.text: How many triples $(x,y,n)$ are there such that $x^n - y^n = 2^{100}$
negative_passages.docid: 55266
negative_passages.text: Prove that $(n+1)^{n-1}<n^n$