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24553Re: 2.75 selfridge program

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  • paulunderwooduk
    Oct 9, 2012
      I need to report an of error:

      > for odd n with minimal x such that kronecker(x^2-4,n)==-1,
      >
      > if x=0 then 2 selfridge:
      > (L+2)^(n+1)==5 (mod n, L^2+1)
      >
      > if x=1 then 3 selfridge:
      > gcd(7,n)==1
      > 3^((n-1)/2)==kronecker(3,n) (mod n)
      > L^((n+1)/2)==kronecker(3,n) (mod n, L^2-(2/7)*L+1)

      This should be L^((n+1)/2)==kronecker(7,n) (mod n, L^2-(2/7)*L+1)

      >
      > if x=3 then 4 selfridge:
      > gcd(3,n)==1
      > 3^(n-1)==1 (mod n)
      > 5^((n-1)/2)==-1 (mod n)
      > L^((n+1)/2)==kronecker(-1,n) (mod n, L^2+18*L+1)
      >
      > if n>x>3 then 4 selfridge:
      > (L+2)^(n+1)==5+2*x (mod n, L^2-x*L+1)
      > (L-2)^(n+1)==5-2*x (mod n, L^2-x*L+1)
      >
      > This program is on average (1/2)*2+(1/2)*((1/2)*3+(1/2)*((1/2)*4+(1/2)*4)==2.75 selfridges.
      >
      > It is a mix of "section 10" of my paper in the file section of this group:
      > http://tech.groups.yahoo.com/group/primenumbers/files/Articles/
      > and of http://tech.groups.yahoo.com/group/primenumbers/message/24525
      >
      > Paul
      >
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