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Question Number 200175 by mokys last updated on 15/Nov/23

find all values of x if x^2 ≡4mod(5) and 0≤x≤11 ?

$${find}\:{all}\:{values}\:{of}\:{x}\:{if}\:{x}^{\mathrm{2}} \equiv\mathrm{4}{mod}\left(\mathrm{5}\right)\:{and}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{11}\:? \\ $$

Commented by mokys last updated on 15/Nov/23

where steps of the solution

$${where}\:{steps}\:{of}\:{the}\:{solution} \\ $$

Answered by cortano12 last updated on 15/Nov/23

 x= 8    x=3

$$\:\mathrm{x}=\:\mathrm{8}\: \\ $$$$\:\mathrm{x}=\mathrm{3}\: \\ $$

Answered by Rasheed.Sindhi last updated on 15/Nov/23

x^2 ≡4(mod5)  x≡2(mod 5) ∨ x≡−2(mod 5  x≡2≡7(mod5) ∨ x≡3≡8(mod 5)  x=2,3,7,8

$${x}^{\mathrm{2}} \equiv\mathrm{4}\left({mod}\mathrm{5}\right) \\ $$$${x}\equiv\mathrm{2}\left({mod}\:\mathrm{5}\right)\:\vee\:{x}\equiv−\mathrm{2}\left({mod}\:\mathrm{5}\right. \\ $$$${x}\equiv\mathrm{2}\equiv\mathrm{7}\left({mod}\mathrm{5}\right)\:\vee\:{x}\equiv\mathrm{3}\equiv\mathrm{8}\left({mod}\:\mathrm{5}\right) \\ $$$${x}=\mathrm{2},\mathrm{3},\mathrm{7},\mathrm{8} \\ $$

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