Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By princeps

Math Help - Contest problem 6

  1. #1
    Junior Member Kanwar245's Avatar
    Joined
    Jun 2011
    From
    Canada
    Posts
    68
    Thanks
    2

    Contest problem 6

    Find all positive numbers N with the following property: The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67

    Re: Contest problem 6

    Why are these being answered...I thought it was forbidden to post "contest" problems here.

    Not only that, but Kanwar shows no work....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member Kanwar245's Avatar
    Joined
    Jun 2011
    From
    Canada
    Posts
    68
    Thanks
    2

    Re: Contest problem 6

    these are practice problems sir
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67

    Re: Contest problem 6

    Well, anybody can say that...I didn't make the existing rule...I'm just a helper...
    Perhaps better NOT to use the word "contest"....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: Contest problem 6

    Quote Originally Posted by Kanwar245 View Post
    Find all positive numbers N with the following property: The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
    Up to 10000 the only number with such property is 24 .

    Small Maple program :

    Code:
    for N from 1 to 10000 do
    for i from 2 to N do
    if N mod i = 0 then
    a:=i:
    break;
    end if;
    end do;
    for j from N-1 to 2 by -1 do
    if N mod j = 0 then
    b:=j:
    break;
    end if;
    end do;
    if b=6*a then
    print(N);
    end if;
    end do;
    Thanks from Kanwar245
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,099
    Thanks
    67

    Re: Contest problem 6

    Quote Originally Posted by Kanwar245 View Post
    Find all positive numbers N with the following property:
    The greatest factor of N (other than N) is 6 times the smallest divisor of N (other than 1).
    Well, since no moderator has jumped in with the eviction papers, looks like that
    rule has now been abolished....so:

    u = greatest factor, v = lowest factor

    If N is even, then no choice: v = 2 and u = N/2
    So N/2 = 6v
    N/2 = 12
    N = 24

    If N is odd, then u and v will be odd
    But 6*(odd number) = even
    So none if N is odd.

    Heretoforth, henceforth and allforths, only N=24 is solution.
    Last edited by Wilmer; March 16th 2012 at 09:18 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Contest problem 3
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: March 21st 2012, 01:05 PM
  2. Contest problem 5
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: March 15th 2012, 10:47 AM
  3. Contest problem 2
    Posted in the Math Topics Forum
    Replies: 4
    Last Post: March 13th 2012, 12:52 PM
  4. Contest problem
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: March 12th 2012, 07:51 AM
  5. [SOLVED] Another problem from a USA contest
    Posted in the Advanced Math Topics Forum
    Replies: 6
    Last Post: January 10th 2011, 07:27 PM

Search Tags


/mathhelpforum @mathhelpforum