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Search: Posts Made By: bhelmes
Forum: Hardware 2022-08-02, 03:39
Replies: 158
Views: 22,263
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: 5
Views: 748
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: 5
Views: 748
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: 158
Views: 22,263
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: 435
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: 2,147
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: 2,147
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: 2,147
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: 2,147
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: 2,147
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: 916
Views: 101,117
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: 896
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: 2,933
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: 668
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: 896
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: 2,933
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: 2,933
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: 2,933
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: 2,933
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)
Forum: Number Theory Discussion Group 2022-02-28, 08:46
Replies: 10
Views: 2,933
Posted By bhelmes
E should be the unit matrix (1;0;0;1) and...

E should be the unit matrix (1;0;0;1)

and there might be something similar to a p-1 test factorisation.
Perhaps I have reinvented a pollard p-1 test.
But at least I would know how fast my...
Forum: Number Theory Discussion Group 2022-02-28, 01:09
Replies: 10
Views: 2,933
Posted By bhelmes
factorisation for M^p=E mod f

A peaceful night for you,

Let M be a 2x2 matrix and p a prime with p>2 and f the number which should be factorized.
If I have succesful found a M and p with M^p=E mod f,
is there a way to detect...
Forum: MattcAnderson 2022-02-15, 01:30
Replies: 3
Views: 250
Posted By bhelmes
if p | f(n) then p | f(n+p) Think about it.

if p | f(n) then p | f(n+p)
Think about it.
Forum: Number Theory Discussion Group 2022-02-14, 05:10
Replies: 4
Views: 1,970
Posted By bhelmes
Considering the matrix M of the form (n²+1; n)...

Considering the matrix M of the form
(n²+1; n)
(n; 1)

=(a; b)
(c; d)

The determinant is one.

For n=0 it includes the neutral element concerning the multiplication,
Forum: Lounge 2022-02-13, 23:43
Replies: 916
Views: 101,117
Posted By bhelmes
You just might be addicted to GIMPS if you note...

You just might be addicted to GIMPS if you note happily that your house has a 100 amper fuse by 220 volt and you ask all your 14 neighbours in the house if they could reduce their power consumption,...
Forum: Number Theory Discussion Group 2022-02-12, 04:08
Replies: 1
Views: 475
Posted By bhelmes
hensel lifting or chinese remainder

A peaceful and pleasant night for you,

I know the hensel lifting in order to lift a zero point of a polynomial to a zero point of order 2.
Is it possible to get the same result with the chinese...
Showing results 1 to 25 of 404

 
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