Ivan Shishkin, Rye (1878)

Problems/Arithmetic

A characterization of rational numbers

by T.W·translated by Ancient Tree·
23
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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English
EnglishFrançais

Let x∈Rx\in\mathbb R. Prove that xx is a rational number if and only if its base-1010 expansion is eventually periodic.

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