query: Prove that p(x) cannot have more than m zeros , where $p(x)$ is a polynominal of degree m and $p(x) ∈ \mathbb{K} [x]$ and $\mathbb{K}$ is a field
positive_passages.docid: 62134
positive_passages.text: Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
negative_passages.docid: 10514
negative_passages.text: Proof that no polynomial with integer coefficients can only produce primes
negative_passages.docid: 120627
negative_passages.text: Reducibility of polynomials modulo p
negative_passages.docid: 129050
negative_passages.text: Find the number of non-zero squares in the field $Zp$
negative_passages.docid: 37183
negative_passages.text: Show that the set of all $x$ such that $x \in P$ and $x \notin Q$ exists
negative_passages.docid: 27577
negative_passages.text: An irreducible polynomial of degree coprime to the degree of an extension is irreducible over this extension
negative_passages.docid: 121304
negative_passages.text: Is the set of polynomials of degree less than or equal to $n$ closed?
negative_passages.docid: 154487
negative_passages.text: Maximal number of monomials of multivariate polynomial
negative_passages.docid: 154507
negative_passages.text: If all the roots of a polynomial P(z) have negative real parts, prove that all the roots of P'(z) also have negative real parts
negative_passages.docid: 88036
negative_passages.text: Prove that if $p \equiv 3 \pmod{4}$ then $x^2+y^2 \not \equiv 0 \pmod{p}$
negative_passages.docid: 56898
negative_passages.text: Number of monomials of certain degree
negative_passages.docid: 98577
negative_passages.text: Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
negative_passages.docid: 148910
negative_passages.text: Multivariate polynomials have infinitely many zeroes
negative_passages.docid: 46821
negative_passages.text: Finding roots in $\mathbb{Z}_p$
negative_passages.docid: 70463
negative_passages.text: Let $p$ be prime and $a$ be a natural not divisible by $p$. Then, $\exists$ integers $x,y$ such that $ax\equiv y \pmod{p}$ with $0<|x|,|y|<\sqrt{p}$
negative_passages.docid: 135385
negative_passages.text: $0 < a_0 \leq a_1 \leq \cdots \leq a_n$, show $ p_n(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_{n-1} z + a_n = 0$ has no root in $|z| < 1$
negative_passages.docid: 68124
negative_passages.text: why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$