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Re: A prove about Euler number

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  • Andrew Swallow
    Bill, I ve looked around a little. I m not sure about part (b) of your question, since it looks a little strange to me. But anyway. As for part (a), I d
    Message 1 of 2 , Jun 28, 2003
      Bill,

      I've looked around a little. I'm not sure about part (b) of your
      question, since it looks a little strange to me. But anyway.

      As for part (a), I'd suggest you look up the topic of 'primitive
      roots' in any good number theory book. I have a proof in front of me
      of the non-existence of primitive roots for a certain type of moduli,
      and the proof uses something very similar to your number 'U'.

      (If you want specifics, the book is that of Niven, Zuckerman &
      Montgomery, & I'm looking at the proof of Thm 2.41. )

      Hope this is of help, sorry I can't say much about part (b)!

      Andy

      --- In primenumbers@yahoogroups.com, "Bill" <iampoliceman@y...> wrote:
      > let n = (P1^k1)(P2^k2)....(Pl^kl) where the Pi's are distinct primes
      > and where each Ki >= 1,and let U = lcm(O(P1^k1),...,O(Pl^kl)), where
      > O is the Euler number.
      >
      > a) show that if gcd(a,n) = 1, then a^U = 1 (mod n)
      > b) show that for any a we have a^(U+m) = a^m (mod n), where m = max
      > {k1,k2,k3,...,kl}
      >
      > any help is greatly appreicated!!! thanks
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