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Results tagged with polynomials
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user 4140
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
4
votes
1
answer
413
views
Convergence of the Double Integral of a Polynomial Reciprocal
Let $f \in \mathbb{R}[x,y]$ be a polynomial satisfying the following conditions:
(i) $f(\mathbb{R}^2) \subset [a,\infty)$ where $a>0$;
(ii) $f$ is non-degenerate, in the sense that there isn't a non …
- 3,142
9
votes
Accepted
Set of primes dividing polynomials and composition
I guess this answer complements Gene's answer above. Here is an example to think about. Let
$$
A=(x^2-2)(x^2-17)(x^2-34).
$$
It's an easy exercise in quadratic reciprocity to show that $\mathcal{P}(A) …
- 3,142
3
votes
2
answers
486
views
Positivity of a finite sum
Define polynomials
$$
U(x)=(x+i-1)^k
$$
and
$$
V(x)=x(x+1)\cdots(x+i-1).
$$
Let $Q$ and $R$ be the quotient and remainder on dividing $U$ by $V$. The above sum is the leading coefficient of $R$. …
- 3,142