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Homework 1: Division and modularity

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Find the following without using a calculator (show all steps):
(5^2 mod 13)^3 mod 7
(3^3 mod 11)^2 mod 5
(2^4 mod 5)^4 mod 3
Show whether the following is true or false:
12≅5(mod 7)
13≅2(mod 11)
100≅3(mod 13)
Calculate the following:
100 mod 5
12 mod 7
85 mod 13
Give the set Z_7

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