Notes:Modulo rings

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System Add Multiply
[ilmath]\text{Mod}\ (7)[/ilmath]
[ilmath]+[/ilmath] [ilmath]0[/ilmath] [ilmath]1[/ilmath] [ilmath]2[/ilmath] [ilmath]3[/ilmath]
[ilmath]0[/ilmath] 0 1 2 3 4 5 6
[ilmath]1[/ilmath]
[ilmath]\text{Mod}\ (6)[/ilmath]

Mod 7

+ 0 1 2 3 4 5 6
0 0 1 2 3 4 5 6
1 1 2 3 4 5 6 0
2 2 3 4 5 6 0 1
3 3 4 5 6 0 1 2
4 4 5 6 0 1 2 3
5 5 6 0 1 2 3 4
6 6 0 1 2 3 4 5

x 0 1 2 3 4 5 6
0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6
2 0 2 4 6 1 3 5
3 0 3 6 2 5 1 4
4 0 4 1 5 2 6 3
5 0 5 3 1 6 4 2
6 0 6 5 4 3 2 1

Mod 6

+ 0 1 2 3 4 5
0 0 1 2 3 4 5
1 1 2 3 4 5 0
2 2 3 4 5 0 1
3 3 4 5 0 1 2
4 4 5 0 1 2 3
5 5 0 1 2 3 4
x|0_1_2_3_4_5
0|0 0 0 0 0 0
1|0 1 2 3 4 5
2|0 2 4 0 2 4
3|0 3 0 3 0 3
4|0 4 2 0 4 2
5|0 5 4 3 2 1