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Theorem about Fermats last

  1. Nov 30, 2008 #1

    disregardthat

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    I read in a book about Fermats last theorem that it has been proved that "if there are solutions to the equation a^n+b^n=c^n, then there are only a finite number of them". I searched this up and found this article:

    http://findarticles.com/p/articles/mi_m1200/is_n12_v133/ai_6519267

    A quote from the article states:

    How can this be?
    Suppose [tex]a_0, b_0[/tex] and [tex]c_0[/tex] are solutions to the equation [tex]a^n+b^n=c^n[/tex] for a specified n, i.e [tex]a_0^n+b_0^n=c_0^n[/tex]. But by multiplying by [tex]k^n[/tex] where k is a natural number larger than 1 yields [tex](a_0k)^n+(b_0k)^n=(c_0k)^n[/tex] which is a different solution. This is true for all values of k larger than 1, so I cannot see how the theorem is true.

    Please clarify!
     
  2. jcsd
  3. Nov 30, 2008 #2

    morphism

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    There's (probably) the unstated assumption that gcd(a,b,c)=1.
     
  4. Nov 30, 2008 #3

    disregardthat

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    Yes, I thought of that, but I didn't see it anywhere. It is most likely true though.
     
  5. Nov 30, 2008 #4
    There are 0 solutions, so it is definitely (not most likely) true!
     
  6. Nov 30, 2008 #5

    disregardthat

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    Of course =), but before fermats was proven this theorem was probably of importance.
     
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