Question Number 200175 by mokys last updated on 15/Nov/23
$${find}\:{all}\:{values}\:{of}\:{x}\:{if}\:{x}^{\mathrm{2}} \equiv\mathrm{4}{mod}\left(\mathrm{5}\right)\:{and}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{11}\:? \\ $$
Commented by AST last updated on 15/Nov/23
$$\mathrm{2},\mathrm{3},\mathrm{7},\mathrm{8} \\ $$
Commented by mokys last updated on 15/Nov/23
$${where}\:{steps}\:{of}\:{the}\:{solution} \\ $$
Answered by cortano12 last updated on 15/Nov/23
$$\:\mathrm{x}=\:\mathrm{8}\: \\ $$$$\:\mathrm{x}=\mathrm{3}\: \\ $$
Answered by Rasheed.Sindhi last updated on 15/Nov/23
$${x}^{\mathrm{2}} \equiv\mathrm{4}\left({mod}\mathrm{5}\right) \\ $$$${x}\equiv\mathrm{2}\left({mod}\:\mathrm{5}\right)\:\vee\:{x}\equiv−\mathrm{2}\left({mod}\:\mathrm{5}\right. \\ $$$${x}\equiv\mathrm{2}\equiv\mathrm{7}\left({mod}\mathrm{5}\right)\:\vee\:{x}\equiv\mathrm{3}\equiv\mathrm{8}\left({mod}\:\mathrm{5}\right) \\ $$$${x}=\mathrm{2},\mathrm{3},\mathrm{7},\mathrm{8} \\ $$