mod arithmetic question (1 Viewer)

[underthesun]

Just wondering, are we able to assume: (or is this the definition)
a = b (mod m)

means

a = km + b

where k is an integer?

It's for this question where I have to prove that:

if a = b (mod m) then gcd(a, m) = gcd(b, m).

Simple, but I've been skipping maths lectures

 

[Affinity]

from what you have

a = km + b

b = a - km

b is divisible by gcd(a,m)
similarly
a is divisible by gcd(b.m)

so gcd(a,m), gcd(b,m) are divisors of a,b and m

so gcd(a,m)<= gcd(b,m)
also gcd(b,m) <= gcd(a,m)
hence we conclude they are equal.

good luck next week

 

[underthesun]

Thanks . It's for discrete maths, but good luck for algebra too (you won't really need it though..)

You must be doing higher maths, but are you in higher computing as well? Cuz if you are, you happen to be in my class .

 

[Affinity]

don't you guys have a DM test next week? I thought I heard that from my mates.

 

[McLake]

Originally posted by underthesun
Just wondering, are we able to assume: (or is this the definition)
a = b (mod m)

means

a = km + b

where k is an integer?

If you havn't already been shown this, you will be soon. It's a valid assumption ...

 

[underthesun]

Originally posted by McLake
If you havn't already been shown this, you will be soon. It's a valid assumption ...

I just felt asleep during lectures

Originally posted by Affinity
don't you guys have a DM test next week? I thought I heard that from my mates.

That test was last week. Well.. good thing it's only very small %, so I dont have to make big deals out of my losses..