Tìm n thuộc N a) n + 6 chia hết n b) 4n + 5 chia hết cho n c) 38 – 3n chia hết cho n d) n + 5 chia hết n + 1 e) 3n + 4 chia hết n – 1 g) 2n + 1 chia h

Đáp án:

 

Giải thích các bước giải:

 $n+6$ $\vdots$ $n$

$⇒6$ $\vdots$ $n$

$⇒n∈${$6;3;2;1;-1;-2;-3;-6$}

Mà $n∈N$

$⇒n∈${$6;3;2;1$}

$ $

$4n+5$ $\vdots$ $n$

$⇒5$ $\vdots$ $n$

$⇒n∈${$5;1;-1;-5$}

Mà $n∈N$

$⇒n∈${$5;1$}

$ $

$38-3n$ $\vdots $n$

$⇒38$ $\vdots$ $n$

$⇒n∈${$38;19;1;-1;-19;-38$}

Mà $n∈N$

$⇒n∈${$38;19;1$}

$ $

$n+5$ $\vdots$ $n+1$

$⇒(n+1)+4$ $\vdots$ $n+1$

$⇒4$ $\vdots$ $n+1$

$⇒n+1∈${$4;2;1;-1;-2;-4$}

$⇒n∈${$3;1;0;-2;-3;-5$}

Mà $n∈N$

$⇒n∈${$3;1;0$}

$ $

$3n+4$ $\vdots$ $n-1$

$⇒3n-3+3+4$ $\vdots$ $n-1$

$⇒3.(n-1)+7$ $\vdots$ $n-1$

$⇒7$ $\vdots$ $n-1$

$⇒n-1∈${$7;1;-1;-7$}

$⇒n∈${$8;2;0;-6$}

Mà $n∈N$

$⇒n∈${$8;2;0$}

$ $

$2n+1$ $\vdots$ $16-3n$

$⇒3.(2n+1)+2.(16-3n)$ $\vdots$ $16-3n$

$⇒6n+3+32-6n$ $\vdots$ $16-3n$

$⇒35$ $\vdots$ $16-3n$

$⇒16-3n∈${$35;7;5;1;-1;-5;-7;-35$}

$⇒3n∈${$-19;9;11;15;17;21;23;51$}

$⇒n∈${$\frac{-19}{3};3;\frac{11}{3};5;\frac{17}{3};7;\frac{23}{3};17$}

Mà $n∈N$

$⇒n∈${$3;5;7;17$}

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