Question

3 power 2012 in decimal notation

Answer 1

Answer:

Since φ(100) = φ(2^2) φ(5^2) = (2^2 - 2)(5^2 - 5) = 40.

So, 3^40 = 1 (mod 100) by Euler's Theorem.

Therefore, 3^(2012)

= 3^(40 * 50 + 12)

= (3^40)^50 * 3^12

= 1^50 * (3^6)^2

= 29^2

= 41 (mod 100), choice