Ivan Shishkin, Rye (1878)

Problems/ArithmeticUnreviewed

Jamais deux (carrés) sans trois

by budleya·
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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Soit a,ba,b DEUX entiers strictement positifs. On suppose que la somme a2+b2a^{2}+b^{2} de leurs CARRÉS est divisible par ab+1ab+1. Montrer que a2+b2ab+1\displaystyle{a^2+b^2 \over ab+1} est un carré.

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