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Search: Posts Made By: bhelmes
Forum: Number Theory Discussion Group 2022-11-24, 22:52
Replies: 15
Views: 3,021
Posted By bhelmes
A prediction of the rotation matrices

There should be more peace in the world !

The pythagorean triples can be used to make a surjective mapping to the rotation matrices concerning p

if x²+y²=z² | : z²
(x/z)²+(y/z)²=1 which is the...
Forum: Miscellaneous Math 2022-11-16, 17:27
Replies: 8
Views: 538
Posted By bhelmes
The polynomial f(n)=n²-n+41 has the discriminant...

The polynomial f(n)=n²-n+41 has the discriminant b²-4c=1-4*41=-163,

For this special case I recommend a sieve procedure similar like the sieve of Eratosthenes:...
Forum: Number Theory Discussion Group 2022-11-03, 01:35
Replies: 4
Views: 1,057
Posted By bhelmes
A peaceful and pleasant night for all members,...

A peaceful and pleasant night for all members, especially for Dr Sardonicus,

I appreciate really your mathematical explications.



If I calculate a/b=a*b^(-1) mod p. Is this an advantage,...
Forum: Number Theory Discussion Group 2022-10-24, 23:03
Replies: 4
Views: 1,057
Posted By bhelmes
Two months later, 270 views and 0 reply for a at...

Two months later, 270 views and 0 reply for a at least nice idea for a mersenne probabilistic prime test,
Is it worth to make an implementation or should I save my time for more interesting work ?...
Forum: Forum Feedback 2022-10-17, 20:15
Replies: 3
Views: 907
Posted By bhelmes
life and future as mathematician

A peaceful and delightful night for you, wherever you stay

is there a real chance to get a half time job at a university with homeoffice, like Rwth Aachen, without a diplom,
but perhaps after...
Forum: Number Theory Discussion Group 2022-10-02, 21:22
Replies: 15
Views: 3,021
Posted By bhelmes
A prediction of a rotation matrix for Mp

A peaceful and pleasant night for you,

If Mp is a Mersenne number with exponent p
I can predict the following rotation matrix

M=(Mp-2^[(p-1)/2];-2^[(p-1)/2)
(2^[(p-1)/2]; Mp-2^[(p-1)/2])...
Forum: Number Theory Discussion Group 2022-09-22, 03:01
Replies: 15
Views: 3,021
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: 15
Views: 3,021
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: 15
Views: 3,021
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: 879
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: 15
Views: 3,021
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: 4
Views: 1,057
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: 25,826
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: 15
Views: 3,021
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: 15
Views: 3,021
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: 25,826
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: 837
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: 2,822
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: 2,822
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: 2,822
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: 2,822
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: 2,822
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: 924
Views: 107,109
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: 1,080
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: 4,067
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:...
Showing results 1 to 25 of 416

 
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