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Forum: Number Theory Discussion Group 2022-09-22, 03:01
Replies: 12
Views: 1,452
Posted By bhelmes
Is it possible to calculate one belonging rot. matrix from a vector ?

A peaceful, early morning, especially for Dr Sardonicus,

let: p=31, u1=2, v1=3; so that the norm (u1,v1)=u1²+v1²=13=12⁻¹ mod 31 and 13²=20⁻¹ mod 31

Is it possible from linear algebra to...
Forum: Number Theory Discussion Group 2022-09-18, 23:23
Replies: 12
Views: 1,452
Posted By bhelmes
Every matrix M of the form (x -y) (y x) ...

Every matrix M of the form
(x -y)
(y x)
with determinant (M)=x²+y² can be transformed by a scalar multiplication of the matrix by the inverse of the determinant
into a rotation matrix with...
Forum: Number Theory Discussion Group 2022-09-17, 01:02
Replies: 12
Views: 1,452
Posted By bhelmes
Basic rotation matrixes

A peaceful night for you, where ever you sleep,

Are there three basic rotation matrices, like

E =
(1 0) = Identity with determinant (E) = 1
(0 1)

M1 =
(1 -1) with determinant (M1) = 2
Forum: Homework Help 2022-09-08, 19:37
Replies: 0
Views: 337
Posted By bhelmes
rational points on the unit circle / rotation matrix

A peaceful and pleasant night for you, wherever you stay

if p is a prime > 3 and
all calculation is performed by modulo p
then all rational points u/v
with the same norm n=u²+v² and
as non...
Forum: Number Theory Discussion Group 2022-08-20, 01:18
Replies: 12
Views: 1,452
Posted By bhelmes
A peaceful and pleasant night for you, this...

A peaceful and pleasant night for you,

this is a beautiful and colored representation of numbers with the according rotation matrixs.
It is not perfect, but I thought LaurV or Serge could use...
Forum: Number Theory Discussion Group 2022-08-17, 20:00
Replies: 0
Views: 212
Posted By bhelmes
a suggestion for a fast probablistic prime test

A peaceful night for you,

Imho this is a nice piece of math, a suggestion for a fast probablistic prime test,
perhaps the finding of two suitable bases with the same norm can be improved,...
Forum: Hardware 2022-08-02, 03:39
Replies: 163
Views: 23,892
Posted By bhelmes
The good news is that in Germany the EEG-taxes...

The good news is that in Germany the EEG-taxes were canceled and the price for a kwh drops from 29 cent to 26 cent,
which will count for me up to 31.8.


The bad news is that my electric provider...
Forum: Number Theory Discussion Group 2022-07-23, 06:23
Replies: 12
Views: 1,452
Posted By bhelmes
There is a logical error in my thinking and I...

There is a logical error in my thinking and I could not solve the paradox :

a:=4+5i, b:=8+15i
If I regard the euklidean norm of both vectors:
||a||=sqrt (16+25)=sqrt (41)
||b||=sqrt...
Forum: Number Theory Discussion Group 2022-07-20, 14:07
Replies: 12
Views: 1,452
Posted By bhelmes
rotation matrix

A peaceful night for you,

the weather in Germany was yesterday and today a little bit hot,
which is not ideal for me to think about math.
Normally I prefer a temperature under 25 degree in the...
Forum: Hardware 2022-07-11, 19:37
Replies: 163
Views: 23,892
Posted By bhelmes
A peaceful day for you, my electrical bill...

A peaceful day for you,

my electrical bill for the last year will come soon and I searched the actual price for 1 kWh:
I saw two companies in Germany which offer 1kWh for 0,49 Euro instead of...
Forum: Number Theory Discussion Group 2022-06-28, 20:48
Replies: 1
Views: 593
Posted By bhelmes
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...
Forum: Number Theory Discussion Group 2022-06-08, 11:44
Replies: 18
Views: 2,462
Posted By bhelmes
A peaceful and pleasant day for you, I miss...

A peaceful and pleasant day for you,

I miss the case
4. g=1 and f odd

I am searching for x²+y²=m²+n²=d mod f, resp. two sums of squares with the same norm d mod f.

Algorithm:
choose a...
Forum: Number Theory Discussion Group 2022-06-04, 18:25
Replies: 18
Views: 2,462
Posted By bhelmes
A peaceful day for you, Is there a known...

A peaceful day for you,

Is there a known algorithm for
x²+y²=m²+n²=d mod f

I think it is easier than to find x²+y²=0 mod p

Any interesting suggestion how to speed up Gimps ?
I really need...
Forum: Number Theory Discussion Group 2022-05-19, 23:50
Replies: 18
Views: 2,462
Posted By bhelmes
A peaceful and pleasant night for you, if a...

A peaceful and pleasant night for you,

if a compositon of n=x²+y² exists and n not a prime,
how many different compostions exist depending of the number of factors of n ?

Please have patience...
Forum: Number Theory Discussion Group 2022-05-07, 00:26
Replies: 18
Views: 2,462
Posted By bhelmes
I only needed one composition and the algorithm...

I only needed one composition and the algorithm is described under
https://en.wikipedia.org/wiki/Fermat%27s_theorem_on_sums_of_two_squares

The english version of wikipedia is much better than the...
Forum: Number Theory Discussion Group 2022-05-04, 23:38
Replies: 18
Views: 2,462
Posted By bhelmes
n=a²+b²

A peaceful and pleasant night for you,

if n odd and not a square and n, a, b element N
how do I find (fast) the composition n=a²+b² ?

Thanks in advance if you spent me some lines or a link.
...
Forum: Lounge 2022-04-15, 23:21
Replies: 921
Views: 102,836
Posted By bhelmes
You just might be addicted to GIMPS if you are...

You just might be addicted to GIMPS if you are desperated that there is still no new Mp.
As you know that your computer can run 5% faster if you decrease the temperature by 10 degree,
you bay a...
Forum: Miscellaneous Math 2022-04-02, 00:42
Replies: 2
Views: 955
Posted By bhelmes
After removing some bugs and some duplicates it...

After removing some bugs and some duplicates it looks nicer:

http://devalco.de/matrix_with_det_1/system_matrix_with_det_1.php

The matrixs mod p, with p=3 mod 4 look o.k.

but the other...
Forum: Number Theory Discussion Group 2022-03-24, 23:12
Replies: 10
Views: 3,069
Posted By bhelmes
if det (M)=1 and M symmetric and M<>E you can...

if det (M)=1 and M symmetric and M<>E
you can diagonalize M to M',
where still M'^p=E mod f and the det (M')<>1

Nevertheless my implementation fails for M149 and I know why.


:redface:...
Forum: Lounge 2022-03-10, 20:34
Replies: 9
Views: 688
Posted By bhelmes
I prefer juggling, 5 balls if I am warmed up. ...

I prefer juggling, 5 balls if I am warmed up.
http://rabbitweb.de


There was a time, I tried to make a living from juggling. I can teach it and tried four schools.
One hour juggling is a good...
Forum: Miscellaneous Math 2022-03-10, 02:54
Replies: 2
Views: 955
Posted By bhelmes
visualisations of primes / cycle representations

A peaceful night for you,

this is a visualisation for the exponentation of 2*2 matrixs with determant 1 mod f.
I think it is mathematical correct, but perhaps there might be a more beautiful...
Forum: Number Theory Discussion Group 2022-03-08, 04:43
Replies: 10
Views: 3,069
Posted By bhelmes
If I limit the 2x2matrixs to those with...

If I limit the 2x2matrixs to those with determinant equal 1, your sentence is of course right.
Unfortenately I see no way to get a factorisation result of f.

Is there a known factorisation...
Forum: Number Theory Discussion Group 2022-03-03, 23:12
Replies: 10
Views: 3,069
Posted By bhelmes
This is a try for a visulisation of 2x2 matrixs...

This is a try for a visulisation of 2x2 matrixs with determinant of 1 and their exponentation modulo p:
http://devalco.de/matrix_with_det_1/system_matrix_with_det_1.php


If you have an idea for...
Forum: Number Theory Discussion Group 2022-03-02, 03:04
Replies: 10
Views: 3,069
Posted By bhelmes
It is amazing and beautiful. One mathematical...

It is amazing and beautiful. One mathematical sentence which explains everything.

Thanks a lot for this clear and fruitful explication.


:bow::hello::cmd::uncwilly:

P.S. I am on vacation,...
Forum: Number Theory Discussion Group 2022-02-28, 11:15
Replies: 10
Views: 3,069
Posted By bhelmes
I do matrix multiplication and at the end I...

I do matrix multiplication and at the end I calculate every element mod f:

M:=
(a; b)
(c; d)

M mod f :=
(a mod f; b mod f)
(c mod f; d mod f)
Showing results 1 to 25 of 410

 
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