query: does $x-y$ divide $x^{2k-1}-y^{2k-1}$ for all $k\in \mathbb{N}$?
positive_passages.docid: 2522
positive_passages.text: Why is $a^n - b^n$ divisible by $a-b$?
negative_passages.docid: 74150
negative_passages.text: Problem on the number of generators of some ideals in $k[x,y,z]$
negative_passages.docid: 70522
negative_passages.text: $y^2 = \frac{x^5 - 1}{x-1}$ & $x,y \in \mathbb{Z}$
negative_passages.docid: 98921
negative_passages.text: Does $y(y+1) \leq (x+1)^2$ imply $y(y-1) \leq x^2$?
negative_passages.docid: 5595
negative_passages.text: $x^y = y^x$ for integers $x$ and $y$
negative_passages.docid: 100984
negative_passages.text: Prove that if prime $p$ divide $a_{2k}-2$, then $p$ divide also $a_{2k+1}-1$.
negative_passages.docid: 143543
negative_passages.text: Prove that $(n - 1)^2 \mid n^k -1$ if and only if $(n - 1) \mid k$
negative_passages.docid: 104987
negative_passages.text: Equivalence Relation with dividing x and y integers
negative_passages.docid: 464
negative_passages.text: Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
negative_passages.docid: 156671
negative_passages.text: Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
negative_passages.docid: 13572
negative_passages.text: $x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
negative_passages.docid: 146093
negative_passages.text: Why if $n \mid m$, then $(a^n-1) \mid (a^m-1)$?
negative_passages.docid: 15191
negative_passages.text: If $a^2$ divides $b^2$, then $a$ divides $b$
negative_passages.docid: 135046
negative_passages.text: Can this quick way of showing that $K[X,Y]/(Y-X^2)\cong K[X]$ be turned into a valid argument?
negative_passages.docid: 9997
negative_passages.text: For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
negative_passages.docid: 29452
negative_passages.text: Divisor in $\mathbb{C}[X]$ $\implies$ divisor in $\mathbb{R}[X]$?
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?