Ivan Shishkin, Birch Grove

Théorème des restes chinois

Theorem / Group / Stub

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Also known as: Théorème chinois

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Soient nn et mm deux entiers supérieurs ou égaux à 1.
Alors, on a l'isomorphisme :
Z/nZ×Z/mZ≅Z/nmZ\Z/n\Z\times \Z/m\Z\cong \Z/nm\Zsi et seulement si nn et mm sont premiers entre eux.

Practice this concept with exercises

  • Les isomorphismes de groupes suivants sont-ils vrais :

    1. Z/5Z≅Z/2Z×Z/3Z\Z/5\Z \cong \Z/ 2\Z \times \Z/3\Z ?

    2. Z/6Z≅Z/2Z×Z/3Z\Z/6\Z \cong \Z/ 2\Z \times \Z/3\Z ?

    3. Z/4Z≅Z/2Z×Z/2Z\Z/4\Z \cong \Z/ 2\Z \times \Z/2\Z ?

    Open exerciseDifficulty 36/100 · 1 solution · 0 hints
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