## Curious Equation

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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
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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• ... 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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