Question Number 120471 by mathocean1 last updated on 31/Oct/20
![solve in Z x^3 +2x+1≡1[4]](Q120471.png)
$${solve}\:{in}\:\mathbb{Z}\:{x}^{\mathrm{3}} +\mathrm{2}{x}+\mathrm{1}\equiv\mathrm{1}\left[\mathrm{4}\right] \\ $$
Answered by Ar Brandon last updated on 31/Oct/20
![x^3 +2x+1=1[4]⇒x^3 +2x=0[4] ⇒x^3 +2x=4k, k∈Z x=2m, m∈Z](Q120473.png)
$$\mathrm{x}^{\mathrm{3}} +\mathrm{2x}+\mathrm{1}=\mathrm{1}\left[\mathrm{4}\right]\Rightarrow\mathrm{x}^{\mathrm{3}} +\mathrm{2x}=\mathrm{0}\left[\mathrm{4}\right] \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{3}} +\mathrm{2x}=\mathrm{4k},\:\mathrm{k}\in\mathbb{Z} \\ $$$$\mathrm{x}=\mathrm{2m},\:\mathrm{m}\in\mathbb{Z} \\ $$