Results 1 to 3 of 3

Math Help - Modulo proof help2

  1. #1
    Newbie
    Joined
    Jul 2008
    Posts
    13

    Modulo proof help2

    Let n be a positive integer. Prove that 1+2+3.....+(n-1) =0mod n if and only if n is odd.

    I assumed first that 1 +2+3...+(n-1)=o mod n. Show n is odd. We know by the Appendix that 1+2+3...+n= [n(n+1)]\2
    I plugged n-1 into n in the above equation. which is [n(n-1)]/2. Now do I let that be congruent to 0modn?!?

    If you could help I would really appreciate it! Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6
    Quote Originally Posted by kel1487 View Post
    Let n be a positive integer. Prove that 1+2+3.....+(n-1) =0mod n if and only if n is odd.

    I assumed first that 1 +2+3...+(n-1)=o mod n. Show n is odd. We know by the Appendix that 1+2+3...+n= [n(n+1)]\2
    I plugged n-1 into n in the above equation. which is [n(n-1)]/2. Now do I let that be congruent to 0modn?!?

    If you could help I would really appreciate it! Thanks!
    Actually its simple if you observe that 2 divides n-1 iff n is odd.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member PaulRS's Avatar
    Joined
    Oct 2007
    Posts
    571
    Note that: 1+2+...+(n-2)+(n-1)=[(n-1)+1]+[(n-2)+2]+...+\left[\left(n-\frac{n-1}{2}\right)+\frac{n-1}{2}\right] if n is odd

    If n is even: 1+2+...+(n-2)+(n-1)=[(n-1)+1]+[(n-2)+2]+...+\left[\left(n-\frac{n-2}{2}\right)+\frac{n-2}{2}\right]+\frac{n}{2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modulo Question: Proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 20th 2010, 06:14 PM
  2. Modulo Proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: December 7th 2009, 09:52 AM
  3. Congruence & Modulo Proof
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 15th 2009, 06:00 PM
  4. Modulo proof
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: July 16th 2008, 04:22 PM
  5. Modulo proof help
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 14th 2008, 06:24 PM

Search Tags


/mathhelpforum @mathhelpforum