Ivan Shishkin, Rye (1878)

Problems/Polynomial

Polynômes réels positifs

by Sequoia·
40
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.
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ReviewedReviewed by Ancient Tree
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Français
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This problem was submitted to “The two squares”.

Showing the Français version because no English translation exists yet. Add that translation.

Soit P∈R[X]P\in\R[X] un polynôme tel que P(X)⩾0P(X)\geqslant0 pour tout x∈Rx\in\R.

Montrer que PP est la somme de deux carrés de deux polynômes, soit qu’il existe A,B∈R[X]A,B\in\R[X] tels que P=A2+B2P=A^2+B^2.

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