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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.

1 vote
0 answers
471 views

The mysterious numbers $ \frac{13}{20} $ and $20$?

Let $g(x) = x^6 - 30 x $ Let $h(x) = x^6 $ Let $f(x) = x^2 - 2 $ Let $r$ be a reduced fraction $0 < \frac{p}{q} < 2 $ with integers $p,q > 1$ Let $f_{n+1}(x) = f(f_n(x)) = f_n(f(x)) , f_0(x) = x$ …
mick's user avatar
  • 769
13 votes
3 answers
716 views

Supremum of $ a_n = a_{n-1}^3 - a_{n-2} $

Let $a_1=0$ and let $ - \ln(2) < a_2 < \ln(2) $ Define $$ a_n = a_{n-1}^3 - a_{n-2} $$ Then $$ \sup_{n>2} a_n = a_2 $$ And $$ \inf_{n>2} a_n = - a_2 $$ How to prove that ?
mick's user avatar
  • 769
4 votes
1 answer
167 views

When is a solution $P(f'(x)) = Q(f(x))$ periodic or double periodic?

operatorname{cl}}\newcommand{\sl}{\operatorname{sl}}\newcommand{\cm}{\operatorname{cm}}\newcommand{\sm}{\operatorname{cm}}$Consider the differential equation $$P(f '(x)) = Q(f(x))$$ Where $P(x),Q(x)$ are polynomials … Does every pair of polynomials $P,Q$ with degrees between $2$ and $4$ give double periodic functions? Are degrees above $4$ possible to get double periodic functions? …
mick's user avatar
  • 769