Ivan Shishkin, Rye (1878)

Problems/General algebraReviewed

nn points sur le cercle unité

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50
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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Soient A1,…,AnA_1, \ldots, A_n des points du cercle unité de R2\mathbb{R}^2. Montrer l’existence de MM sur ce cercle tel que
MA1×⋯×MAn=1.M A_1 \times \cdots \times M A_n=1.

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