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If $4x\equiv 8\pmod{20}$ and $3x\equiv 16\pmod{20}$, then what is the remainder when $x^2$ is divided by $20$?

 

tysm!

 Dec 24, 2020
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Using "CRT + MMI", we have:

 

(4 x) mod 20 = 8
(3 x) mod 20 = 16, solve for x

 

x = 20m + 12, where m = 0, 1, 2, 3.........etc.

x =20 * 1  +  12 = 32

 

x^2 =32^2 mod 20 == 4 - The remainder.

 Dec 24, 2020

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