Toán Lớp 6: Tìm số dư trong phép chia 3^2023 + 7 cho 80
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Toán Lớp 6: Tìm số dư trong phép chia 3^2023 + 7 cho 80
Comments ( 1 )
Ta có : 3^4 ≡ 1 ( mod 80 )
⇒ ( 3^4 )^505 ≡ 1^505 ( mod 80 )
⇔ 3^2020 ≡ 1 ( mod 80 )
⇔ 3^2020 . 3^3 ≡ 1 . 3^3 ( mod 80 )
⇔ 3^2023 ≡ 27 ( mod 80 )
⇔ 3^2023 + 7 ≡ 27 + 7 ( mod 80 )
⇔ 3^2023 + 7 ≡ 34 ( mod 80 )
⇒ 3^2023 + 7 chia 8 dư 34