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Curious Equation

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  • Sebastian Martin
    Hello all:     Find all solutions of this equation:   Sqrt[p(x)*p(x+y)-1]= y   p(x)=x-th prime;  Sqrt=Square Root           I have found tree
    Message 1 of 2 , Aug 22, 2008
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      Hello all:
       
       
      Find all solutions of this equation:
       
      Sqrt[p(x)*p(x+y)-1]= y
       
      p(x)=x-th prime;  Sqrt=Square Root
       
       
       
       
       
      I have found tree solutions:
       
      x=1 y=5   Sqrt[p(1)*p(1+5)-1]=Sqrt[2*13-1]=Sqrt[25]=5
       
      x=3 y=22
       
      x=10  y=186
       
      Sincerely:
       Sebastian Martin Ruiz

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    • Paul Leyland
      ... Interesting question. I suspect that there are only finitely many more solutions, perhaps no more, but don t have a clue how to start to prove this. Paul
      Message 2 of 2 , Aug 22, 2008
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        On Fri, 2008-08-22 at 02:20 -0700, Sebastian Martin wrote:
        > Hello all:
        >
        >
        > Find all solutions of this equation:
        >
        > Sqrt[p(x)*p(x+y)-1]= y
        >
        > p(x)=x-th prime; Sqrt=Square Root
        >
        >
        >
        >
        >
        > I have found tree solutions:
        >
        > x=1 y=5 Sqrt[p(1)*p(1+5)-1]=Sqrt[2*13-1]=Sqrt[25]=5
        >
        > x=3 y=22
        >
        > x=10 y=186

        Interesting question. I suspect that there are only finitely many more
        solutions, perhaps no more, but don't have a clue how to start to prove
        this.


        Paul
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