Ivan Shishkin, Rye (1878)

Problems/Real analysisUnreviewed

Contraintes intégrales

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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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Soit nn un entier impair supérieur ou égal à 3 . Déterminer les fonctions continues ff de [0,1][0,1] dans R\mathbb{R} telles que, pour tout k∈⟦1,n−1⟧k \in \llbracket 1, n-1 \rrbracket$,
∫01(f(x1/k))n−k dx=kn.\int_0^1\left(f\left(x^{1 / k}\right)\right)^{n-k} \mathrm{~d} x=\frac{k}{n}.

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References

  1. Oral ENS 2025
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