Results 1 to 6 of 6

Math Help - Canonical Decomp

  1. #1
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5

    Canonical Decomp

    2^{27}+1=(2^9)^3+1^3=(2^9+1)(2^{18}-2^9+1) =(2^3+1)(2^6-2^3+1)(2^{18}-2^9+1)

    What next?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    It looks like you can write 2^3+1=(2+1)(2^2-2+1).

    Is this what you are aiming for?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    No, this section:
    (2^6-2^3+1)(2^{18}-2^9+1)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member roninpro's Avatar
    Joined
    Nov 2009
    Posts
    485
    As polynomials, you can't factor those anymore.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    I have broken it down to 3^3*19*(2^9*7*73+1) but it isn't fully decomp.

    What to do next?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    2^n is congruent to \pm1 mod 3, according as n is even or odd. So 2^{18}-2^9+1 is a multiple of 3. In fact it is equal to 3*87211, and 87211 is prime, as you can check here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. canonical parameter and canonical link function
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 6th 2011, 08:41 AM
  2. Canonical Decomp 2
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: June 19th 2010, 10:56 AM
  3. LU Decomp Question
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 27th 2010, 01:31 PM
  4. prime power decomp
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 5th 2008, 08:05 PM
  5. Help with Partial Fraction Decomp
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 9th 2007, 07:05 AM

/mathhelpforum @mathhelpforum