Ivan Shishkin, Rye (1878)

Problems/Number theoryReviewed

Even-odd equality

by Ancient Tree·
10
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.
·
English
EnglishFrançais

Suppose that

ab=cdab=cd

where aa and cc are even integers, while bb and dd are odd integers.
Is it necessarily the case that a=ca=c and b=db=d ?

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Solution by CypressFR

Discussions1 useful vote

Un contre-exemple simple est de prendre a=2, b=9, c=6 et d=3. On a bien ab=cd=18. Mais on a : a ≠ c et b ≠ d. L’affirmation est donc fausse.

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