- 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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[Non-text portions of this message have been removed] - On Fri, 2008-08-22 at 02:20 -0700, Sebastian Martin wrote:
> Hello all:

Interesting question. I suspect that there are only finitely many more

>

>

> 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

solutions, perhaps no more, but don't have a clue how to start to prove

this.

Paul