 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/5/a/i/solution

Z_{3} = {0, 1, 2}

, perform ordinary addition and multiplication and then take the remainder modulo

3

. The tables are

+ 012 001211202201 \cdot 012 000010122021 .

The nonzero elements have multiplicative inverses

1^{- 1} = 1

and

2^{- 1} = 2

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