Results 1 to 2 of 2

Math Help - Automorphic Numbers

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    144

    Automorphic Numbers

    An automorphic number reappears at the end of its square. Disregarding 0 and 1, the only one-digit automorphic numbers are 5 and 6 since 5 = 25, and 6 = 36. Find all two-digit and three-digit automorphic numbers.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2008
    From
    Melbourne Australia
    Posts
    210
    Thanks
    22
    Some thoughts

    let a be the automorphic number exceeding 9, then a*(a-1) is divisible by 100.

    Therefore, a Xor a-1 is divisible by 2.
    Therefore, a Xor a-1 is divisible by 4

    Similarly
    a or a-1 is divisible by 25.

    Now a little trial and error:
    a=25 works
    49,50,51 don't divide by 4
    a=76 works

    let a be the automorphic number exceeding 99, then a*(a-1) is divisible by 1000.
    Therefore, a Xor a-1 is divisible by 8.

    Similarly
    a or a-1 is divisible by 125.

    A little more trial and error turns up two more automorphic numbers.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: August 29th 2011, 02:18 AM
  2. Automorphic Numbers
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: February 8th 2011, 12:41 PM
  3. Replies: 1
    Last Post: September 27th 2010, 03:14 PM
  4. Derivative of an automorphic rational function
    Posted in the Math Challenge Problems Forum
    Replies: 1
    Last Post: June 19th 2010, 07:34 AM
  5. Replies: 3
    Last Post: April 10th 2008, 05:58 PM

Search Tags


/mathhelpforum @mathhelpforum