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24825Re: mod quartic composite tests

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  • djbroadhurst
    Jan 18, 2013
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      > All are trapped by Paul's latest wriggle,
      > which requires x^2-3 to be coprime to n.

      Exercise: Show that Paul's test
      Mod(Mod(1,n)*(L+x^2-2),(L^2-x*L+1)*(L^2+x*L+1))^n==-L^3+(x^2-2)*L+x^2-2
      requires n to be a Fermat pseudoprime in base 1+(x^2-3)*(x^2-2)^3
      and thus loses (at least) one selfridge of potency for x^2 = 3 mod n.

      David
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