Answer to Question #313959 in Discrete Mathematics for Bij8

Question #313959

Value of 3^222mod11




1
Expert's answer
2022-03-19T02:37:19-0400

Since gcd(3,11)=1\gcd(3,11)=1 and φ(11)=10,\varphi(11)=10, by Euler's Theorem we get that 310=1mod  11.3^{10}=1 \mod 11.

Therefore,

3222mod  11=(310)2232mod  11=1229mod  11=9.3^{222}\mod11=(3^{10})^{22}\cdot 3^2\mod 11=1^{22}\cdot 9\mod 11=9.



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