Question

Fie mulțimea
A={x | x € N și (x+1) | (x+7) }
Aflați x.

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Answer 1

A={1,2,3,4... | 7,8,9,10...}

Answer 2

   
[tex]\displaystyle \\ x\in N~si~(x+1)~|~(x+7) ~ \Longleftrightarrow~ (x+7)~\vdots~ (x+1) ~ \Longleftrightarrow ~ \frac{x+7}{x+1} \in N \\ \\ \frac{x+7}{x+1} = \frac{x+1+6}{x+1}= \frac{x+1}{x+1}+\frac{6}{x+1} = 1+\frac{6}{x+1} \\ \\ D_6 = \{1;~2;~3;~6\} \\ x+1=1 ~ \Longrightarrow ~ x_1 = 0\\ x+1=2 ~ \Longrightarrow ~ x_2 = 1\\ x+1=3 ~ \Longrightarrow ~ x_3 = 2\\ x+1=6~ \Longrightarrow ~ x_4 = 5\\ \Longrightarrow ~ x \in \{0;~1;~2;~5\}[/tex]