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5-10-mod-11-




Question Number 95868 by rb222 last updated on 28/May/20
5^(10) (mod 11)=?
$$\mathrm{5}^{\mathrm{10}} \left({mod}\:\mathrm{11}\right)=? \\ $$
Commented by Rasheed.Sindhi last updated on 28/May/20
5^5 ≡1(mod 11)  (5^5 )^2 ≡(1)^2 (mod 11)  5^(10) ≡1(mod 11)
$$\mathrm{5}^{\mathrm{5}} \equiv\mathrm{1}\left({mod}\:\mathrm{11}\right) \\ $$$$\left(\mathrm{5}^{\mathrm{5}} \right)^{\mathrm{2}} \equiv\left(\mathrm{1}\right)^{\mathrm{2}} \left({mod}\:\mathrm{11}\right) \\ $$$$\mathrm{5}^{\mathrm{10}} \equiv\mathrm{1}\left({mod}\:\mathrm{11}\right) \\ $$
Answered by i jagooll last updated on 28/May/20
1 (mod 11)
$$\mathrm{1}\:\left(\mathrm{mod}\:\mathrm{11}\right) \\ $$

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