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Thread: Is this Correct?

  1. #1
    rcs
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    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 ?
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  2. #2
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    Re: Is this Correct?

    Quote Originally Posted by rcs View Post
    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]
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  3. #3
    rcs
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    Re: Is this Correct?

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