Tìm x ∈ Z để A ∈ Z x+2003 A= x

2 câu trả lời

`A=(x+2003)/x=x/x+2003/x=1+2003/x`

`text(để A nguyên khi )2003/xtext( nguyên)`

`=>2003vdotsx=>x in Ư_((2003))={+-1:+-2003}`

`text( ta có bảng sau)`

$\begin{array}{|c|c|}\hline x&-2003&-1&1&2003\\\hline \dfrac{2003}{x}&-1&-2003&2003&1\\\hline A&-2&-2004&2002&0\\\hline \end{array}$

`text(Vậy A )={-2004;-2;0;2002} text( thì )x={-2003;-1;1;2003}`

Ta co $A = 1 + \dfrac{2003}{x}$

De $A \in Z$ thi x la uoc cua 2003.

Do 2003 la so nguyen to nen $x = \pm 1, \pm 2003$.

Vay $A = 2004, -2002, 2, 0$.