2022-06-28, 20:48 | #1 |
Mar 2016
2^{2}·101 Posts |
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. Last fiddled with by bhelmes on 2022-06-28 at 20:49 |
2022-07-01, 06:51 | #2 |
"Matthew Anderson"
Dec 2010
Oregon, USA
5×233 Posts |
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 https://reference.wolfram.com/language/guide/GroupTheory.html https://www.youtube.com/watch?v=zkADn-9wEgc You may need a reference on Abstract Algebra I no longer have all of my textbooks. I'm 'living the life of Riley'. |
Thread Tools | |
Similar Threads | ||||
Thread | Thread Starter | Forum | Replies | Last Post |
PRP residue question | Ensigm | Data | 1 | 2020-08-15 12:22 |
prime generators for quadric irreducible polynomials | bhelmes | Computer Science & Computational Number Theory | 122 | 2017-08-25 21:09 |
Primes on quadric irreducible polynomials | henryzz | Puzzles | 2 | 2013-02-17 05:27 |
Quadratic residue mod 2^p-1 | alpertron | Miscellaneous Math | 17 | 2012-04-30 15:28 |
Residue classes | CRGreathouse | Math | 4 | 2009-03-12 16:00 |