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Re: puzzle for a counterexample

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  • djbroadhurst
    ... Here are 5 such counterexamples, in the format [n, a, t]: [921244609, 52198420, 515951943] [2544329101, 263357820, 100205789] [11273067541, 703848073,
    Message 1 of 66 , Nov 1, 2012
      --- In primenumbers@yahoogroups.com,
      "bhelmes_1" <bhelmes@...> wrote:

      > If you find one counterexample of the form n=1 mod 4
      > i would be glad to know it.

      Here are 5 such counterexamples, in the format [n, a, t]:

      [921244609, 52198420, 515951943]
      [2544329101, 263357820, 100205789]
      [11273067541, 703848073, 6861362057]
      [27536216921, 12158783674, 18501786352]
      [30048858209, 9925760819, 22855838720]

      David
    • djbroadhurst
      ... Here are some scores out of 5: {A(k,x)=sum(j=0,k/2,(-1)^j*binomial(k-j,j)*x^(k-2*j));} {B(k,x)=sum(j=0,(k-1)/2,(-1)^j*binomial(k-j-1,j)*x^(k-2*j-1));}
      Message 66 of 66 , Nov 22, 2012
        --- In primenumbers@yahoogroups.com,
        paulunderwooduk" <paulunderwood@...> wrote:

        > At least one of the evaluations of x at -1,1,0,-2 or 2
        > should be -1,1,0,-2, or 2

        Here are some scores out of 5:

        {A(k,x)=sum(j=0,k/2,(-1)^j*binomial(k-j,j)*x^(k-2*j));}
        {B(k,x)=sum(j=0,(k-1)/2,(-1)^j*binomial(k-j-1,j)*x^(k-2*j-1));}
        {L=[-1,1,0,-2,2];S=Set(L);for(k=2,40,f=factor(A(k,x)-B(k,x))[,1];
        g=f[#f];c=0;for(j=1,#L,if(setsearch(S,subst(g,x,L[j])),c++));
        print1(c","));}

        4,4,3,4,4,4,4,4,4,4,4,3,4,4,4,5,4,4,4,4,5,4,4,4,4,5,4,4,4,5,5,4,4,4,4,4,5,4,3,

        David
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