Question

Texts: Mod Powers Let n be any positive number. Consider the following congruence 108^(n) ≡ r (mod 11), where r is the remainder when 108^(n) is divided by 11. a) First, let's recall the meaning of the word "remainder." The remainder when dividing by 11 is an integer that could be as small as 0 or as large as 10. b) Next, we will reduce the base. What is the remainder when 108 is divided by 11? c) Next, we find the size of the loop. In the given congruence, how many distinct solutions for r exist whenever n > 99? d) Finally, what is the remainder when 108^(160) is divided by 11?

          Texts: Mod Powers

Let n be any positive number. Consider the following congruence 108^(n) ≡ r (mod 11), where r is the remainder when 108^(n) is divided by 11.

a) First, let's recall the meaning of the word "remainder." The remainder when dividing by 11 is an integer that could be as small as 0 or as large as 10.

b) Next, we will reduce the base. What is the remainder when 108 is divided by 11?

c) Next, we find the size of the loop. In the given congruence, how many distinct solutions for r exist whenever n > 99?

d) Finally, what is the remainder when 108^(160) is divided by 11?

Added by Lawrence G.

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