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Carmichael number

  1. Dec 1, 2008 #1
    $n=pqr$ is a Carmichael number. If $q-1|pr-1$ and $r-1|pq-1$ then show that q-1 is a divisor in
    $(d+p)(p-1).$
     
  2. jcsd
  3. Dec 1, 2008 #2
    ok here it is the clear version of it.

    n=pqr is carmicahelnumber. if we have that r-1|pq-1 then I have shown that
    pq-1=d(r-1) where d is [2;p-1]. Moreover I have shown that q-1|d(r-1)-p+1.
    Now I want to show that if q-1|pr-1 is also fulfilled then q-1 is divisor in (d+p)(p-1). Do you understand it?
     
  4. Dec 14, 2008 #3
    Hi!
    I suggest you to read more before publish your problems since this is a very well known question (Wikipedia).
     
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