Toán CMR: $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ chia hết cho 271(n > 0) 11/07/2021 By Nevaeh CMR: $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ chia hết cho 271(n > 0)
Đáp án: `2090^n-803^n-464^n+261^n vdots 271` Giải thích các bước giải: `2090≡193(mod271)` `=>2090^n≡193^n(mod271)` Hoàn toàn tương tự: `=>803^n≡261^n(mod271)` `=>464^n≡193^n(mod271)` `=>261^n≡261^n(mod271)` `=>2090^n-803^n-464^n+261^n≡193^n-261^n-193^n+261^n(mod271)` `=>2090^n-803^n-464^n+261^n≡0(mod271)` `=>2090^n-803^n-464^n+261^n vdots 271` Trả lời
Giải thích các bước giải: Ta có: ⊕ 2090 ≡ 193 (mod 271) ⇒ $2090^{n}$ ≡ $193^{n}$ (mod 271) ⊕ 803 ≡ 261 (mod 271) ⇒ $803^{n}$ ≡ $261^{n}$ (mod 271) ⊕ 464≡ 193 (mod 271) ⇒ $464^{n}$ ≡ $193^{n}$ (mod 271) ⊕ $261^{n}$ ≡ $261^{n}$ (mod 271) ⇒ $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ ≡ $193^{n}$ – $261^{n}$ – $193^{n}$ + $261^{n}$ (mod 271) ≡ 0 (mod 271) ⇒ $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ chia hết cho 271 (đpcm) Trả lời
Đáp án:
`2090^n-803^n-464^n+261^n vdots 271`
Giải thích các bước giải:
`2090≡193(mod271)`
`=>2090^n≡193^n(mod271)`
Hoàn toàn tương tự:
`=>803^n≡261^n(mod271)`
`=>464^n≡193^n(mod271)`
`=>261^n≡261^n(mod271)`
`=>2090^n-803^n-464^n+261^n≡193^n-261^n-193^n+261^n(mod271)`
`=>2090^n-803^n-464^n+261^n≡0(mod271)`
`=>2090^n-803^n-464^n+261^n vdots 271`
Giải thích các bước giải:
Ta có:
⊕ 2090 ≡ 193 (mod 271) ⇒ $2090^{n}$ ≡ $193^{n}$ (mod 271)
⊕ 803 ≡ 261 (mod 271) ⇒ $803^{n}$ ≡ $261^{n}$ (mod 271)
⊕ 464≡ 193 (mod 271) ⇒ $464^{n}$ ≡ $193^{n}$ (mod 271)
⊕ $261^{n}$ ≡ $261^{n}$ (mod 271)
⇒ $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ ≡ $193^{n}$ – $261^{n}$ – $193^{n}$ + $261^{n}$ (mod 271) ≡ 0 (mod 271)
⇒ $2090^{n}$ – $803^{n}$ – $464^{n}$ + $261^{n}$ chia hết cho 271 (đpcm)