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3^201 mod 11 =

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in Cryptograph & Network Security by (60.1k points)
3^201 mod 11 =

(a) 3

(b) 5

(c) 6

(d) 10

I got this question during an online exam.

Question is from Number Theory in portion More Number Theory of Cryptograph & Network Security

1 Answer

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Best answer
The correct choice is (a) 3

The explanation is: Use Fermats Theorum. Fermat’s Theorem states that if p is prime and a is a positive integer not divisible

by p, then a^(p–1) = 1 (mod p). Therefore 3^10 = 1 (mod 11). Therefore

3^201 = (3^10)^20 x 3 = 3 (mod 11).

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