voi x,y thuoc Z, 7x+3y chia het cho 13 ⇔ 5x+4y chia het cho 13

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1. $\,\,\,\,\,\,7x+3y\,\,\,\vdots \,\,\,13$

   $\to 10\left( 7x+3y \right)\,\,\,\vdots \,\,\,\,13$

   $\to 70x+30y\,\,\,\vdots \,\,\,13$

   $\to 70x+30y-13.5x-13.2y\,\,\,\vdots \,\,\,13$

   $\to 70x+30y-65x-26y\,\,\,\vdots \,\,\,13$

   $\to 5x-4y\,\,\,\vdots \,\,\,13$

    

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2. – Xét tổng :

   `3(7x+3y)+(5x+4y)`

   `=21x+9y+5x+4y`

   `=(21x+5x)+(9y+4y)`

   `=26x+13y`

   `=13(2x+y) vdots 13`

   `=> 3(7x+3y)+(5x+4y) vdots 13`

   mà `3(7x+3y) vdots 13`

   `=> 5x+4y vdots 13  text{(đpcm)}`

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