compute 9^301 mod 11

Question

Hello ,

 

I want help with this compute 9^301 mod 11

 

thanks

Answer 1

Observe that you are asked to find 3^602 mod 11.

In a manner similar to the previous congruence question that I answered, make a congruence table of powers of 3.

The pattern of congruences for 3^o thru 3⁴ gives results 1, 3, 9, 5, 4 and then these results repeat periodically.

 

So divide 602 (the exponent on 3 in this problem) by 5, capturing only the remainder as exponent 0 thru 4, and thus identify the answer.