Question

I'm having trouble with modular arithmetic. There are the problems:

Answer 1

HI!!

Answer 2

Hello.

Answer 3

work directly from the definition
that is what you have to do

Answer 4

is a ≡ b (mod m) the same as m|(a − b).?

Answer 5

are these equal to each other?

Answer 6

\[a\equiv a(\text{mod } m )\] means \(m|a-a\)

Answer 7

yes that is what it means
just notation is all

Answer 8

pretty clear that \(m\) divides \(a-a\) because any number divides zero

Answer 9

now that you know what to do, i am sure you can do the rest

Answer 10

I thought it was m divides (a-b)

Answer 11

Recall that
\[\Large a | b \ \Leftrightarrow \ a*k = b\]
i.e.
`a | b`, or 'a' divides b, is the same as saying 'a' is a factor of b

Answer 12

where k is some integer

Answer 13

yes in general it is
but your first job is to show that \[a\equiv a(\text{mod }m)\]

Answer 14

what exactly is a ≡ b (mod m)? what does that mean?

Answer 15

so where you see a \(b\) put an \(a\) and you get \[m|a-a\]

Answer 16

do you know what \(m|a-b\) means ?

Answer 17

mk= a-b?

Answer 18

for example \[2\equiv 12(\text{mod}5)\] because \[5|12-2\]

Answer 19

that means five goes in to \(12-2\) evenly

Answer 20

or you can put what you wrote, same thing, but for your proof you can use the definition