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A problem with Joseph Rotman's Advanced modern Algebra

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data

    Let [itex]n=p^rm[/itex], where [itex]p[/itex] is a prime not dividing an integer [itex]m>1[/itex]. Prove that

    [itex]p[/itex] does not divide [itex]C_n^{p^r}[/itex].

    2. Relevant equations

    There is a hint: Assume otherwise, cross multiply, and use Euclid's lemma.

    3. The attempt at a solution

    Although the author gives a hint, I still cannot figure out how to use it. I do not know what "cross multiply" means. Can anyone of you tells me? Or, can you give me another hint? Thank you very much!
  2. jcsd
  3. Sep 11, 2011 #2

    Stephen Tashi

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    Science Advisor

    "Cross multiply" is slang for changing an equation like [itex] \frac{a}{b} = \frac{c}{d} [/itex] to the equation [itex] ad = bc [/itex]. I suppose it could also be used to indicate changing an equation like [itex] a = \frac{c}{d} [/itex] to the form [itex] ad = c [/itex].
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