RMS - sequence

[Max Alekseyev]

On Sat, Jun 28, 2008 at 11:40 AM, Ctibor.ZIZKA <Ctibor.ZIZKA at seznam.cz> wrote:

> 2)
>
> Numbers n with 3 divisors. We know n must be of the form p*p which gives
> divisors (1, p, p*p)  :
>
> RMS(n=1*p*p) = sqrt ( (1+p^2+p^4)/2 )  is a positive integer.
>
> I do not know any p for which this equation holds.

First, I think you meant "/3" not "/2".
Second, according to magma, the only integer solutions to
y^2 = (1+x^2+x^4)/3
are (x,y) = (1,1) and (1,-1).

Regards,
Max