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Question
Write the multiplication table for the set of integers modulo 5.
Solution
Here,
1 × 5 1 = Remainder obtained by dividing 1 × 1 by 5
3 × 5 4 = Remainder obtained by dividing 3 × 4 by 5
4 × 5 4 = Remainder obtained by dividing 4 × 4 by 5 = 1
So, the composition table is as follows:
| ×5 | 0 | 1 | 2 | 3 | 4 |
| 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 1 | 2 | 3 | 4 |
| 2 | 0 | 2 | 4 | 1 | 3 |
| 3 | 0 | 3 | 1 | 4 | 2 |
| 4 | 0 | 4 | 3 | 2 | 1 |
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