mersenneforum.org (https://www.mersenneforum.org/index.php)
-   Number Theory Discussion Group (https://www.mersenneforum.org/forumdisplay.php?f=132)
-   -   non quadric residue of Q/Z (https://www.mersenneforum.org/showthread.php?t=27902)

 bhelmes 2022-06-28 20:48

non quadric residue of Q/Z

A peaceful and joyful night for you

if you consider the finite group of rationals modulo p resp. u/v mod p element of Q/Z

Is u/v a non quadratic residue,
if jacobi (u²+v², p)=-1 or
if jacobi (u, p)*jacobi (v, p)=-1

A short answer, perhaps with a little explication, would be very nice and perhaps also interesting for other members.

:redface: :loco::hello::uncwilly:

 MattcAnderson 2022-07-01 06:51

introduction to mathematical groups

Hi bhelmes and others,
You must know about finite cyclic groups.
For example, the simplest group contains only 1 element.
We can call this the identity element, or shorten it to
just one letter 'e'.

The second easiest group is like the odd and the even numbers.
Let's use 'o' for odd and 'e' for even.
We have a finite group under addition.

Other (mathematical) groups can be formed under multiplication,
or a specialty operation

Cheers

[URL="https://reference.wolfram.com/language/guide/GroupTheory.html"]https://reference.wolfram.com/language/guide/GroupTheory.html
[/URL]