query: Suppose p(x) is a polynomial with integer coefficients. Show that if p(a) =1 for some integer a then p(x) has at most two integer roots.
positive_passages.docid: 35478
positive_passages.text: Polynomial $p(a) = 1$, why does it have at most 2 integer roots?
negative_passages.docid: 147047
negative_passages.text: Does there exist a polynomial $p(x) \in \mathbb C[x]$ such that $p(x) \notin \mathbb R[x]$ and $p(x)p(-x)=p(x^2)$?
negative_passages.docid: 109778
negative_passages.text: Proving $(x-c)|(p(x)-p(c))$
negative_passages.docid: 103165
negative_passages.text: the number of the positive integer numbers $k$ that makes for the two quadratic equations $ \pm x^2 \pm px \pm k$ rational roots.
negative_passages.docid: 148458
negative_passages.text: $x^p-x \equiv x(x-1)(x-2)\cdots (x-(p-1))\,\pmod{\!p}$
negative_passages.docid: 107089
negative_passages.text: finding rational roots of polynomials
negative_passages.docid: 155559
negative_passages.text: Quickest way to determine a polynomial with positive integer coefficients
negative_passages.docid: 94682
negative_passages.text: Polynomial: prove there is no double root
negative_passages.docid: 132665
negative_passages.text: Show $p(X)$ (over a field) is irreducible iff $p(X+a)$ is irreducible
negative_passages.docid: 137669
negative_passages.text: $P$ is a monic polynomial of degree $n$ , then which are correct?
negative_passages.docid: 130342
negative_passages.text: Show that for any integer a and prime p, $(a+1)^p \equiv a^p+ 1 \pmod{p}$.
negative_passages.docid: 62134
negative_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: 107765
negative_passages.text: Prove that there exists two roots in $[-1,1]$
negative_passages.docid: 141184
negative_passages.text: Proof that a degree 4 polynomial has at least two roots
negative_passages.docid: 116204
negative_passages.text: Polynomial Remainder Question?
negative_passages.docid: 41193
negative_passages.text: Number of integral roots of a polynomial
negative_passages.docid: 1962
negative_passages.text: Polynomial $P(a)=b,P(b)=c,P(c)=a$