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Carmichael numbers of the form (6n+1)(12n+1)(18n+1)

  1. Nov 27, 2012 #1
    1. The problem statement, all variables and given/known data

    q-1.png

    2. Relevant equations



    3. The attempt at a solution

    I'm fine with the second part (n = 6). But the first part is eluding me, I've been told it's quite simple.

    I feel like it's something to do with the fact that for each prime factor of C_n, p1, p2, p3, we have

    p-1|C_n-1

    But don't really know how to use this.
     
  2. jcsd
  3. Nov 28, 2012 #2

    haruspex

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    Does it help to consider acn-1 mod (6n+1) etc?
     
  4. Nov 28, 2012 #3

    Dick

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    Pick a so that gcd(a,c_n)=1. So gcd(a,p1)=1. So a^(p1-1)=1 mod p1. See a good place to use your divisibility fact?
     
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