Ivan Shishkin, Rye (1878)

Problems/Real analysisReviewed

Polynomials that induce a surjection

by Sequoia·
70
Difficulty scaleÉchelle de difficulté

This score reflects both the level of the required concepts and the difficulty of the solution.Ce score tient compte à la fois du niveau des notions nécessaires et de la difficulté de la résolution.

  1. 1–10First steps / middle schoolPremiers pas / collège
  2. 11–25Beginner / high schoolDébutant / lycée
  3. 26–50Intermediate / undergraduateIntermédiaire / licence
  4. 51–70Advanced / graduateAvancé / master
  5. 71–90Expert / specializedExpert / spécialisé
  6. 91–100Research levelNiveau recherche
These levels are approximate guides.Ces niveaux sont des repères approximatifs.
·
English
EnglishFrançais

Let PP be a complex polynomial. Characterize PP whether it satisfies one of the following surjectivity constraint:

  1. P(C)=CP(\mathbb{C})=\mathbb{C}.
  2. P(R)=RP(\R)=\R.
  3. P(Q)=QP(\mathbb{Q})=\mathbb{Q}.
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