Question

modular arithmetic operations 8 ∙ 8 (mod 6)

I came up with 4 by using a calculator
but if someone could briefly explain what mod is or why to use it that would be awesome!

Answer 1

don't use a calculator

Answer 2

http://www.math.rutgers.edu/~erowland/modulararithmetic.html

Answer 3

im trying really hard to understand, is this right?

8*8(mod6)
64/6=10.66

so the answer is 6?

Answer 4

8*8(mod6) = 64(mod 6) so we can rewrite it as:

64 - 6k = r where k\[k \in Z\] and r is the remainder
so \[\lfloor \frac{ 64 }{ 6 } \rfloor\] = 10 so let k = 10

so 10*6 = 60 so r = 64-60 =4

Answer 5

mod 6 just means that we only have 6 numbers to count with, usually the set: 0,1,2,3,4,5

if we want to count beyond 5, we have to circle about back to the start

0, 1, 2, 3, 4, 5
6, 7, 8, 9, 10, 11

if we want to count beyond 11, we have to circle about back to the start

0, 1, 2, 3, 4, 5
6, 7, 8, 9, 10, 11
12, 13, 14, 15, 16, 17

this cyclical movement defines equivalence classes; for any number in a given column, it is equivalent to (or congruent to) the number presented at the top of the column. notice that the number 8 is in column 2; so we say that 8 is congruent to 2, mod6

8 = 2 mod6

8*8 = 2*2 mod6