Hi guys: Can any one please help me in that problem. I dont understand how this table is created ? Thanks.

Compute the following airthmetic problems in Z/8. Represent answer with the least positive representative of the appropriate equivalence class.

a. [3] + [7]

b. [2] . ([4] + [5])

Addition and multiplication tables for Z/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 2 3 4 5 0

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

Compute the following airthmetic problems in Z/8. Represent answer with the least positive representative of the appropriate equivalence class.

a. [3] + [7]

b. [2] . ([4] + [5])

Addition and multiplication tables for Z/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 2 3 4 5 0

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

0 0 0 0 0 0 0

1

2

3

4

5

i try. In the case of multiplication ist row is all zero:

0*0 =0

in 2nd row. Can you please tell me one more time the second row in the multiplication case

0 0 0 0 0 0 0

1 0 3

2

3

4

5

For 2nd row

1*0 = 0/6 =0

1*1 = 1/6 =

1*2 = 2/6 = 3 reminder

1*4 = 4/6 = 1 reminder

1*5 = 5/6 = 1 reminder

I made mistake

<script>

n=6;

for (i=0;i<n;i++){

for (j=0;j<n;j++)

document.write( (i*j)%n + " ")

document.write("<br>");

}

</script>

Here are the results for n= 6, your table is correct

0 0 0 0 0 0

0 1 2 3 4 5

0 2 4 0 2 4

0 3 0 3 0 3

0 4 2 0 4 2

0 5 4 3 2 1

to get the + table just change i*j to i+j

Any arithmetic mod 6 is simply the remainder after dividing by 6

Note you can add as many 6's as you like when do arithmetic mod 6, as 6 mod 6 = 0

Be careful with negatives though.

eg

(2 - 4 ) mod 6 = - 2 now add 6 onto it give 4 ie the least +ve result,

(3 -2*5) mod 6 = -7 mod 6 = -1 now add 6 to give the least +ve result 5

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you divide by 6 and take the remainder

e.g.

5 x 5 = 25

25 divided by 6 = 4 remainder 1

you only need the '1', as in the table

although some of the values in the 'x' table look wrong, for example 1 x 1 = 1 , not 2 as in the table

_____________________

note also your question asks for z/6, but your tables are z/6

so for z/8, work out then divide by 8, and keep the remainder