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For How Large an 'n' can the Carmichael Function of n be 2?

  1. Jun 4, 2015 #1
    What is the largest n such that λ(n)=2? Is there such a bound? This isn't a homework question. I'm just interested.
     
  2. jcsd
  3. Jun 5, 2015 #2
    If ##p## is not in ##n## than ##(p,n)=1 ##.
    Therefore for ##p^2\equiv 1mod(n)## to hold ##n=6a## since all ##p## other than 2 and 3 are of the form ##6b\pm 1##
    Also all ##p\leq \sqrt{n}## must be in ##n## since otherwise ##p^2<n##.
    so we need a ##p\sharp## such that ##p_{c+1}>\sqrt{p\sharp}##.
    It's easy to see that this does not hold for ##p>5##.
    Therefore the answer is 24.
    [EDIT:-##p\sharp=p_1\times p_2 \times p_3\times.......\times p_c##.]
     
  4. Jun 9, 2015 #3
    Did I scare you off ? I assumed you were familiar with some number theory terminology. If you have any questions, please ask.
     
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