Answer to Question #313959 in Discrete Mathematics for Bij8

Discrete Mathematics

Question #313959

Value of 3^222mod11

Expert's answer

Since "\\gcd(3,11)=1" and "\\varphi(11)=10," by Euler's Theorem we get that "3^{10}=1 \\mod 11."

Therefore,

"3^{222}\\mod11=(3^{10})^{22}\\cdot 3^2\\mod 11=1^{22}\\cdot 9\\mod 11=9."

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