Answers to Practice Problems
1) 3
2) 1
3) 6
4) 0
5) 1
6) 5
7) 1
8) 0
9) 4
10) 3
11) 2
12) 7
13) 2
14) 0
15) 4
16) 1
17) 6
18) 0
19) 7
20) 2
21)
Y = 2x +1 (mod 4)
| X |
Y |
| -4 |
1 |
| -3 |
3 |
| -2 |
1 |
| -1 |
3 |
| 0 |
1 |
| 1 |
3 |
| 2 |
1 |
| 3 |
3 |
| 4 |
1 |
Predictions should continue in the same pattern.
22) X = -2, 2
23) No Solution
24)
Table for Addition in Mod 8
| + |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
| 0 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
| 1 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
0 |
| 2 |
2 |
3 |
4 |
5 |
6 |
7 |
0 |
1 |
| 3 |
3 |
4 |
5 |
6 |
7 |
0 |
1 |
2 |
| 4 |
4 |
5 |
6 |
7 |
0 |
1 |
2 |
3 |
| 5 |
5 |
6 |
7 |
0 |
1 |
2 |
3 |
4 |
| 6 |
6 |
7 |
0 |
1 |
2 |
3 |
4 |
5 |
| 7 |
7 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
The additive inverses of 1, 2, 3, 4, 5, 6, and 7 in mod 8 are 7, 6, 5, 4, 3, 2, and 1, respectively.
There is a pattern. The inverse of n is the mod minus n.
25)
Table for Multiplication in Mod 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 |
The multiplicative inverses of 1, 2, 3, and 4 are 1, 3, 2, and 4, respectively.