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)

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`