Re: Another Quad. Residue question

"Nobody" <STBILLY@xxxxxxxxxxx> wrote in message
news:28135758.1114980680311.JavaMail.jakarta@xxxxxxxxxxxxxxxxxxxxxxxxx
> > "Nobody"
> > > > 1) Is there a good comprehensive source on
> > > > quadratic residues?
> > > > 2) Is it true that given a prime P, then there
> > > > there is between P and
> > > > 2P an (even?) integer for which P is not a
> > > > P is not a quadratic
> > > > residue?
> > > > 3) If 2) is true, can such an integer be
> > > > ger be expressed as a function
> > > > of P.
> > > >
> > > > Thanks much for information.
> > >
> > > If p=3 (mod 4), we can pick p+4.
> > > (Pick p+1 if you want an even integer.)
> > >
> > > If p=1 (mod 4), we can pick p+k,
> > > where k is any quadratic non-residue mod p.
> > > (Pick an odd q.n-r if you want an even integer.)
> > He wants a quadratic *non*-residue.
>
> I thought his question was : find an (even) integer
> n between p and 2p so that p is a q.n-r mod n.
>
> Finding a q.n-r mod p (between p and 2p)
> would be a different problem ...
>
> >Alas there is no
> > known algorithm of any value. Even the very
> > elementary
> > proof that nonsquares exist, and are one-to-one with
> > the
> > squares, is indirect: there are (p-1)/2 squares
> > (omitting
> > zero), and the rest are nonsquares. But how to find
> > a nonsquare without effectively finding *all* the
> > squares? Nobody knows.
> > LH
Yes, sorry, I saw "p" for "q" and vice versa. I suffer slightly
from anno domini.
LH


.

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