query: Bézout's Identity for Polynomial Ring
positive_passages.docid: 72672
positive_passages.text: Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime
negative_passages.docid: 141184
negative_passages.text: Proof that a degree 4 polynomial has at least two roots
negative_passages.docid: 42988
negative_passages.text: Complex polynomial and the unit circle
negative_passages.docid: 117005
negative_passages.text: Rules in the ring with coefficients in finite field $\mathbb{F}_p$
negative_passages.docid: 48977
negative_passages.text: Polynomials having as roots the sum (respectively, the product) of two algebraic elements
negative_passages.docid: 76694
negative_passages.text: Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
negative_passages.docid: 154495
negative_passages.text: Prove that a nontrivial subring of a ring that is a domain has the same identity
negative_passages.docid: 79041
negative_passages.text: What is the formal definition of polynomial ring of several variables?
negative_passages.docid: 155245
negative_passages.text: root of an odd degree polynomial
negative_passages.docid: 103552
negative_passages.text: The minimal polynomial of a primitive $p^{m}$-th root of unity over $\mathbb{Q}_p$
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 158063
negative_passages.text: A formula for the roots of a solvable polynomial
negative_passages.docid: 118532
negative_passages.text: Nilradical of polynomial ring
negative_passages.docid: 154393
negative_passages.text: Roots of polynomial with real coefficients appear in conjugate pairs.
negative_passages.docid: 104233
negative_passages.text: Is the ring of the polynomials on a finite algebraic set always a product of local rings?
negative_passages.docid: 72560
negative_passages.text: Eigenspace of the companion matrix of a monic polynomial
negative_passages.docid: 12079
negative_passages.text: A positive polynomial is the sum of two squares in $\mathbb{R}[X]$