Réponse:
pour que 902⁶⁶+781⁸⁵ soit un multiple de 17,
902⁶⁶+781⁸⁵ = 0(mod17)
From Fermat's little theorem,
902¹⁶ = 1(mod17)
=> 902⁶⁶ = 1(mod17)
781¹⁷ = 781(mod17) = -1(mod17)
=> 781^(17×5) = 781⁸⁵ = (-1)⁵(mod17)
=> 781⁸⁵= -1 (mod17)
Hence, 902⁶⁶+781⁸⁵ = 1+(-1) (mod17) = 0(mod17)
Note: -1(mod17) = 16(mod17)
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Réponse:
pour que 902⁶⁶+781⁸⁵ soit un multiple de 17,
902⁶⁶+781⁸⁵ = 0(mod17)
From Fermat's little theorem,
902¹⁶ = 1(mod17)
=> 902⁶⁶ = 1(mod17)
781¹⁷ = 781(mod17) = -1(mod17)
=> 781^(17×5) = 781⁸⁵ = (-1)⁵(mod17)
=> 781⁸⁵= -1 (mod17)
Hence, 902⁶⁶+781⁸⁵ = 1+(-1) (mod17) = 0(mod17)
Note: -1(mod17) = 16(mod17)