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Canonical Decomp

  1. Jun 18, 2010 #1
    [tex]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)[/tex]

    Now what?
     
  2. jcsd
  3. Jun 18, 2010 #2

    Dick

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    That would really depend a lot on what the question is. Wouldn't it?
     
  4. Jun 18, 2010 #3
    Canonical Decomp.
     
  5. Jun 18, 2010 #4

    Dick

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    I give up. What's Canonical Decomp?
     
  6. Jun 18, 2010 #5

    Canonical Decomp of a [itex]\mathbb{Z}^+[/itex] [itex]n[/itex] is of the form [itex]n=p_{1}^{a_1}*p_{2}^{a_2}\dots p_{k}^{a_k}[/itex], where [itex]p_1,\ p_2, \dots \ p_k[/itex] are distinct primes with [itex]p_1,< p_2, < \dots \ <p_k[/itex] and each exponent is a [itex]\mathbb{Z}^+[/itex]
     
  7. Jun 19, 2010 #6

    Mark44

    Staff: Mentor

    23 + 1 can be factored.
     
  8. Jun 19, 2010 #7

    Mark44

    Staff: Mentor

    Also, 26 - 23 + 1 and 218 - 29 + 1 are not prime.
     
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