Calculer le reste de la division de \(2^{456}\) par\(5\)
On pourra remarquer que \(2^4\equiv 1[5]\)
\(2^{456} = \left(2^4\right)^{114}\). Or \(2^4\equiv 1[5]\) donc \(2^{456} \equiv 1^{114} \equiv 1[5]\)
Calculer le reste de la division de \(2^{437}\) par\(7\)
\(2^3\equiv 1[7]\)
\(2^{437} = 2^{435}+2 = 2^{3\times 145} \times 2^2\)
Donc \(2^{437}\equiv (2^3)^{145} \times 2^2[7]\equiv 1^{145} \times 2^2[7]\equiv 4[7]\)