1.3: Integers Modulo n
1.3: Integers Modulo n
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SOLVED: An integer has a multiplicative inverse modulo n if and only if a and n are relatively prime. So, for each n > 1, we define U(n) to be the set of all positive integers less than and relatively prime to n. Then U(n) is a group under multiplication modulo n. For example, we have U(20) = 1, 3, 7, 9.Construct the Cayley table for U(20). [12 Marks]b. Prove that the set 0, 1, 2, 3 is not a group under multiplication modulo 4. [2 Marks]Why is the set of integers under subtraction not a group? [
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