Re: Another Quad. Residue question

> "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
>
>
.