CMR nếu $x,y\in \mathbb{Z}$ thì $M=(xy-1)(x^{2003}+y^{2003})-(xy+1)(x^{2003}-y^{2003})$ chia hết cho 2

Đáp án:

Ta có : 

`M = (xy – 1)(x^{2003} + y^{2003}) – (xy + 1)(x^{2003} – y^{2003})`

`= xy.(x^{2003} + y^{2003}) – x^{2003} – y^{2003} – xy.(x^{2003} – y^{2003}) – x^{2003} + y^{2003}`

`= [xy.(x^{2003} + y^{2003}) – xy.(x^{2003} – y^{2003})] – (x^{2003} + x^{2003}) + (y^{2003} – y^{2003})`

`= xy.(x^{2003} + y^{2003} – x^{2003} + y^{2003}) – 2.x^{2003}`

`= xy. 2y^{2003} – 2x^{2003}`

`= 2.(xy^{2004} – x^{2003}) ⋮ 2`

`=> đpcm`

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