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Un magicien dit que si :On choisit un nombre premier différent de 2 et 3.On l'élève au carré.On lui ajoute 17.On le divise par 12 et on garde le reste de cette division, alors le reste de cette division vaut 6.(a) Le magicien a-t-il raison ?On rappelle qu'un nombre premier est un nombre qui n'admet que deux diviseurs distincts : 1 et lui-même. Les 10 nombres premiers les plus petits différents de 2 et 3 sont 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.

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