Question

va rog ex 7 dau coronita

Answer 1

   
[tex]\displaystyle\\ \frac{3}{p+1}~~\text{se simplifica, dar numaratorul = 3 care este numar prim.}\\\\ \Longrightarrow~~\frac{3}{p+1}~~\text{se simplifica cu 3.}\\\\ \Longrightarrow~~\boxed{(p+1)~\vdots~3}\\\\ p \ \textgreater \ 2~~\text{ si p este numar natural prim.}\\ \Longrightarrow~~\text{p este numar impar.}\\ \Longrightarrow~~\text{(p + 1)este numar par.}\\\\ \Longrightarrow~~\boxed{(p+1)~\vdots~2 }\\\\ \text{Din: }~~(p+1)~\vdots~3~~\text{si}~~(p+1)~\vdots~2~~ \Longrightarrow~~\boxed{\boxed{(p+1)~\vdots~6}}[/tex]


[tex]\displaystyle\\ \frac{p+7}{6} = \frac{p+1 + 6}{6}\\\\ (p+1)~\vdots~6~~\text{si}~~ 6 ~\vdots~6\\ \Longrightarrow~~\text{Suma lor este divizibila cu 6.}\\ \Longrightarrow~~[(p+1) + 6]~\vdots~6\\ \Longrightarrow~~(p+7)~\vdots~6\\\\ \Longrightarrow~~ \frac{p+7}{6}~~\text{se poate simplifica cu 6.}\\\\ \Longrightarrow~~ \boxed{\boxed{\frac{p+7}{6}\in \mathbb{N}}} [/tex]