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24840Re: mod quartic composite tests

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  • paulunderwooduk
    Jan 27, 2013
      --- In primenumbers@yahoogroups.com, "paulunderwooduk" wrote:

      > Here is another test, on the same theme, for which I cannot also easily find a fraud:
      >
      > {tst(n,x)=kronecker(x^2-4,n)==-1&&
      > gcd(x^2-1,n)==1&&
      > Mod(Mod(1,n)*(L+x^2-1),(L^2-x*L+1)*(L^2+x*L+1))^(n)==-L^3+(x^2-2)*L+x^2-1;}
      >

      n=2953711;x=285843 is a near-counterexample that comes from me testing over the two quadratics that form the quartic. gcd(x,n)==95281 and gcd(x^2-2,n)==31,

      Paul
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