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Results tagged with polynomials
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user 516285
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.
2
votes
1
answer
140
views
Existence of an integer coefficients polynomial with prescribed bounds on [0,4]
Is there a polynomial f with integer coefficients that satisfies the following criteria:
f is not constant;
for all $x\in[0,1]$, $1-\frac{1}{x}\leq f(x)\leq \frac{1}{x}$;
For all $x\in [1,4]$, $0\leq …
- 287
16
votes
1
answer
763
views
Find a special integer coefficients polynomial which takes small absolute value on [0,4]
The question is easy to state: Is there a non-constant $f\in\mathbb{Z}[x]$ such that for all $x\in [0,4]$, we have $|f(x)|\leq 1$? I do not know where to find a useful reference for it.
I did a few tr …
- 287