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7842Re: Factor patterns

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  • djbroadhurst
    Jul 2, 2002
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      > Are there any more numbers sharing this property?
      I believe not; you can do it mod 6, mod 12, mod 24
      and then there are exceptions.
      Easy to see why: we require a modulus M such that
      n^2=1 mod M for all n with gcd(n,M)=1
      M=24 is easy.
      We cannot have any larger M with gcd(M,5)=1,since
      5^2-1=24.
      So try M=12*5.
      Now we have problems with
      7^2-1=48
      unless M=12*5*7.
      Now we have problems with
      11^2-1=120
      It's clear enough that we are are losing out,
      though I do not have a proof..
      David
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