1. ## Is this Correct?

Prove (k,k+1) = 1 for all k element of Z
Let (k, k+1) = d, then d|k and d| k+1
so there exist n, m element of Z s.t. k =dn and k+1 = dm

Now, k +1 = dm
dn + 1 = dm
1 = dm - dn
1 = d ( m -n)
d = db, b (m-b) element of Z

=> d|1
=> d <= 1
but d >= 1. so, d = 1.

Is this Correct? pls correct me if im wrong.. do i miss something ?

2. ## Re: Is this Correct?

Originally Posted by rcs
Prove (k,k+1) = 1 for all k element of Z
Let (k, k+1) = d, then d|k and d| k+1
so there exist n, m element of Z s.t. k =dn and k+1 = dm

Now, k +1 = dm
dn + 1 = dm
1 = dm - dn
1 = d ( m -n)
d = db, b (m-b) element of Z
I'm not sure where "b" came from here. I would use the fact that the only invertible member of Z, with multiplication, is 1 and its inverse is 1. So from 1= d(m- n), it follows that both d and m- n are equal to 1.

=> d|1
=> d <= 1
but d >= 1. so, d = 1.

Is this Correct? pls correct me if im wrong.. do i miss something ?[/QUOTE]

3. ## Re: Is this Correct?

Ooooow i mistyped it.. i should be
1 = d(m-n), whre (m-n) is element of Z