Ivan Shishkin, Rye (1878)

Problems/Linear algebraReviewed

Frobenius sous la trace

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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 pp un nombre premier, AA et BB appartenant à Mn(Z)\mathcal{M}_n(\mathbb{Z}). Montrer que
tr⁡((A+B)p)≡tr⁡(Ap)+tr⁡(Bp)(modp)\operatorname{tr}\big((A+B)^p\big) \equiv \operatorname{tr}\left(A^p\right)+\operatorname{tr}\left(B^p\right)\pmod p

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