query: Is the set of roots unique for each $g(x)$ in $a_n x^n + g(x)$?
positive_passages.docid: 146312
positive_passages.text: Is the set of roots with respect to their values and multiplicies unique for each $g(x)$ in $a_n x^n + g(x)$?
negative_passages.docid: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 81778
negative_passages.text: If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)
negative_passages.docid: 42516
negative_passages.text: If every $x\in X$ is uniquely $x=y+z$ then $\|z\|+\|y\|\leq C\|x\|$
negative_passages.docid: 20438
negative_passages.text: Prove that every positive integer $n$ has a unique expression of the form: $2^{r}m$ where $r\ge 0$ and $m$ is an odd positive integer
negative_passages.docid: 28676
negative_passages.text: Is a finite group uniquely determined by the orders of its elements?
negative_passages.docid: 21363
negative_passages.text: Prove the uniqueness of an inner product
negative_passages.docid: 15109
negative_passages.text: Jordan basis unique?
negative_passages.docid: 72952
negative_passages.text: Uniqueness of a linear map on a basis of a vector space
negative_passages.docid: 88466
negative_passages.text: Show that polynomial $X^{n+1}-aX^n+aX-1$ has only roots of module $1$
negative_passages.docid: 128043
negative_passages.text: $A^n=0$ for $A$ nilpotent without the use of minimal polynomial
negative_passages.docid: 120629
negative_passages.text: Prove if $n$ has a primitive root, then it has exactly $\phi(\phi(n))$ of them
negative_passages.docid: 18108
negative_passages.text: Show if $(a,p)=1$ there is a unique inverse of $a$ modulo $p$
negative_passages.docid: 44100
negative_passages.text: Prove that identity element is unique
negative_passages.docid: 123803
negative_passages.text: If $X^n$ is a diagonal matrix with distinct eigenvalues, then is $X$ also a diagonal matrix with distinct eigenvalues?
negative_passages.docid: 139305
negative_passages.text: Prove $f=1+x+x^2+x^3+\cdots+x^n$ has no multiple roots.
negative_passages.docid: 41486
negative_passages.text: If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer