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More Bernoulli proof

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  • Phil Carmody
    Message 1 of 1 , May 27, 2002
      Here's the outline of another proof valid for even m.
      One can easily show that S(p^r,m)/p^r - S(p^{r+1},m)/p^{r+1}
      is an integer for prime p and r >=1. As S(p^r,m)/p^r -> B_m
      p-adically as r -> infinity then we get
      S(p^r,m)/p^r is an integer for some r >= 1
      S(p^r,m)/p^r is an integer for all r >= 1
      B_m is p-integral.

      Robin Chapman's on form it appears!
      That one looks far simpler for its half of the cases.


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