what can you conclude if a and b are nonzero integers such that a divides b and b divides a?

please helppp

Question

what can you conclude if a and b are nonzero integers such that a divides b and b divides a?

please helppp

wwwhhhaaattt? · Answer

What do you think it is?

anonymous · Answer

its our homework in number theory and i cant anwer this question... its all about divisibility

wwwhhhaaattt? · Answer

Do you know your Times tables?

anonymous · Answer

yeah i knoww.

wwwhhhaaattt? · Answer

Ok, Then I want to see you try.

anonymous · Answer

try? how?

wwwhhhaaattt? · Answer

Try.

anonymous · Answer

like all of em?

jim_thompson5910 · Answer

a divides b means b = a*k for some integer k (basically 'a' is a factor of 'b')
b divides a means a = b*m for some integer m (basically 'b' is a factor of 'a')

wwwhhhaaattt? · Answer

Just try

jim_thompson5910 · Answer

so use the two equations

b = a*k
a = b*m

to help answer the question

jim_thompson5910 · Answer

does that help @alesisaminion ?

anonymous · Answer

@jim_thompson5910 yeah :)) thanks a lot :)xx

jim_thompson5910 · Answer

ok great, I'm glad it does

jim_thompson5910 · Answer

tell me what you can conclude about m and k

anonymous · Answer

@jim_thompson5910 look at your message

jim_thompson5910 · Answer

you should have something along these lines in your steps/work

b = a*k
b = b*m*k ... replace 'a' with 'b*m'
b = b*(m*k)
b/b = [b*(m*k)]/b ... divide both sides by b
1 = m*k
m*k = 1


So I started with one equation, b = a*k, and ended up with m*k = 1. 

If m*k = 1, then what must m and k be? 
Hint: m and k are integers (they can be the same integer)