query: proof of uniqueness of polynomial
positive_passages.docid: 151729
positive_passages.text: Existence of a unique polynomial
negative_passages.docid: 111248
negative_passages.text: The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
negative_passages.docid: 8255
negative_passages.text: Real polynomials from repunits to repunits ( Putnam 2007 A4)
negative_passages.docid: 33011
negative_passages.text: Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
negative_passages.docid: 94682
negative_passages.text: Polynomial: prove there is no double root
negative_passages.docid: 89553
negative_passages.text: proof that every finite matrix has an annihilating polynomial
negative_passages.docid: 111569
negative_passages.text: Property of a polynomial with no positive real roots
negative_passages.docid: 97729
negative_passages.text: Show that a polynomial $f(x)$ over a field $k$ is irreducible if and only if the polynomial $f(x+1)$ is irreducible
negative_passages.docid: 111406
negative_passages.text: Proving that a definition of e is unique
negative_passages.docid: 74452
negative_passages.text: On a uniqueness proof for solutions of $\ a + x = b\,$ in a group
negative_passages.docid: 81682
negative_passages.text: Proving the algebraic set corresponding to a polynomial is infinite.
negative_passages.docid: 156034
negative_passages.text: sufficient condition for a polynomial to have roots in $[0,1]$
negative_passages.docid: 55119
negative_passages.text: Proof that the coefficients of a polynomial are real
negative_passages.docid: 76110
negative_passages.text: Proving that the zero vector is unique
negative_passages.docid: 57368
negative_passages.text: Prove that a positive polynomial function can be written as the squares of two polynomial functions
negative_passages.docid: 40014
negative_passages.text: A polynomial that is zero on an open set
negative_passages.docid: 76955
negative_passages.text: Proof the Legendre polynomial $P_n$ has $n$ distinct real zeros