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.