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Search: Posts Made By: Dr Sardonicus
Forum: Soap Box 2022-09-25, 13:12
Replies: 403
Views: 21,821
Posted By Dr Sardonicus
I thought Uncle Vlad had already persuaded those...

I thought Uncle Vlad had already persuaded those folks to travel and see the world.

Now it seems a lot of would-be conscripts are similarly persuaded.

Unfortunately, many have had to leave with...
Forum: Number Theory Discussion Group 2022-09-25, 00:50
Replies: 12
Views: 1,413
Posted By Dr Sardonicus
It appears you are trying to solve R[a;b] =...

It appears you are trying to solve

R[a;b] = [c;d]

where

R = [x,y;-y,x].

Writing as a system of linear equations,
Forum: jzakiya 2022-09-25, 00:18
Replies: 111
Views: 26,477
Posted By Dr Sardonicus
I've been very reluctant to even respond to these...

I've been very reluctant to even respond to these type of ad hominem statements,[/QUOTE]No. Saying you have no proof is not an "ad hominem statement."

This sort of false accusation is...
Forum: enzocreti 2022-09-23, 17:39
Replies: 2
Views: 85
Posted By Dr Sardonicus
A little algebra may help: 1666667 = (10^7 +...

A little algebra may help:

1666667 = (10^7 + 2)/6

666667 = (2*10^6 +1)/3

2*(10^7 + 2)/6 = (10^7 + 2)/3

(10^7 + 2)/3 = 5*(2*10^6 + 1)/3 - 1
Forum: Proth Prime Search 2022-09-23, 12:21
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
Viewing can make you dumber. We...

Viewing can make you dumber. We agree.[/QUOTE]That's good enough for me.
Forum: Proth Prime Search 2022-09-22, 12:27
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
(my emphasis)

(my emphasis)
Forum: Proth Prime Search 2022-09-21, 13:36
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
Not at all. Let p be a prime number, and let N =...

Not at all. Let p be a prime number, and let N = 2^p - 1.

Then 2^(N-1) == 1 (mod N) [and 2^((N-1)/2) == 1 (mod N) also].

So N "passes" Fermat and Miller-Rabin to the base 2.

So far, only 51...
Forum: Soap Box 2022-09-21, 12:43
Replies: 403
Views: 21,821
Posted By Dr Sardonicus
Calling up 300,000 reservists seven months into...

Calling up 300,000 reservists seven months into the "special military operation" was always part of the plan, of course. Everything's going just fine.

Sounds like sham Anschluss referenda will be...
Forum: Proth Prime Search 2022-09-20, 12:15
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
To the OP: Follow the guidelines in Uncwilly's...

To the OP: Follow the guidelines in Uncwilly's post, link provided for ease of reference. Some of the guidelines you have violated in this thread are quoted below.

Continued violation of...
Forum: Number Theory Discussion Group 2022-09-19, 21:56
Replies: 12
Views: 1,413
Posted By Dr Sardonicus
No, sir. If M is a 2x2 matrix, scalar...

No, sir. If M is a 2x2 matrix, scalar multiplication of M by k produces a matrix with determinant k^2*det(M). Thus, if M is a nonsingular 2x2 matrix, det((1/det(M))M) is 1/det(M).

If M is 2x2...
Forum: Number Theory Discussion Group 2022-09-19, 16:00
Replies: 3
Views: 201
Posted By Dr Sardonicus
:goodposting: Smallest value confirmed. ...

:goodposting:

Smallest value confirmed.

I had Pari-GP find all the liars using CRT as indicated, and also all the plus-or-minus-powers-of-two liars. A bit of abracadabra with sets gave me a...
Forum: Number Theory Discussion Group 2022-09-17, 22:14
Replies: 12
Views: 1,413
Posted By Dr Sardonicus
A rotation matrix has determinant 1 by...

A rotation matrix has determinant 1 by definition, so M1 and M2 are not rotation matrices.

If p is an odd prime, we have seen that if p == 3 (mod 4) there are p+1 rotation matrices (mod p), and if...
Forum: enzocreti 2022-09-15, 13:49
Replies: 1
Views: 258
Posted By Dr Sardonicus
If a congruence holds (mod n), it holds (mod d)...

If a congruence holds (mod n), it holds (mod d) for every divisor d of n. In particular, in the case at hand, as you more or less pointed out in this post...
Forum: Proth Prime Search 2022-09-15, 13:20
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
Please explain the warning about input3.txt ...

Please explain the warning about input3.txt

FWIW I verified that n "passes" the Fermat PRP tests to base 2 and base 14.

When n tests as a Fermat PRP but as composite by Miller-Rabin to the same...
Forum: Lounge 2022-09-14, 13:12
Replies: 13
Views: 431
Posted By Dr Sardonicus
In addition to the perils of mushroom...

In addition to the perils of mushroom misidentification, toxins from fungi (mycotoxins) can be ingested from contaminated food.

One type of such poisoning is called ergotism, or "St. Anthony's...
Forum: Proth Prime Search 2022-09-14, 12:40
Replies: 69
Views: 1,977
Posted By Dr Sardonicus
I see two possibilities here. One is, you don't...

I see two possibilities here. One is, you don't know the definition of "prp test." The other is, you are feigning an ignorance you do not own. Either way, it looks like trolling to me.


If N ==...
Forum: Lounge 2022-09-14, 00:51
Replies: 13
Views: 431
Posted By Dr Sardonicus
I don't forage, but I do know a few "safe"...

I don't forage, but I do know a few "safe" species by sight. One is the puffball (if, as already explained, it isn't "too far along").

Another is a "shelf fungus" called "chicken of the woods." ...
Forum: Lounge 2022-09-12, 19:23
Replies: 1,182
Views: 124,498
Posted By Dr Sardonicus
Jeff Bezos's Blue Origin Shepard 1 booster failed...

Jeff Bezos's Blue Origin Shepard 1 booster failed shortly after liftoff September 12, 2022.

The capsule escape system worked.
Forum: Proth Prime Search 2022-09-12, 14:44
Replies: 19
Views: 1,365
Posted By Dr Sardonicus
At the risk of arrest for criminally re-inventing...

At the risk of arrest for criminally re-inventing the wheel, I give a sketch of a method for finding congruence classes of primes p leading to small prime factors of

x^(2*p-1) - x^(p-1) + 1
...
Forum: Lounge 2022-09-12, 12:49
Replies: 5
Views: 214
Posted By Dr Sardonicus
A cartoonist's legacy lives on!

A cartoonist's legacy lives on!
Forum: Hardware 2022-09-08, 23:55
Replies: 163
Views: 23,812
Posted By Dr Sardonicus
Since the temperature in London hit 40 C (104 F)...

Since the temperature in London hit 40 C (104 F) in late July, that may be understandable. :wink:

However, the usual line I've heard is that it's rainy and chilly there much of the time. Room...
Forum: Lounge 2022-09-08, 23:42
Replies: 16
Views: 208
Posted By Dr Sardonicus
It was NOT Charles III, but Charles II. Charles...

It was NOT Charles III, but Charles II. Charles the III will be the next King. (and perhaps the last one)
<snip>[/QUOTE]The "new monarch" I refer to is the current one. Prince Charles became...
Forum: Puzzles 2022-09-08, 23:37
Replies: 3
Views: 792
Posted By Dr Sardonicus
In Pari-GP scripts, = is an assignment operator. ...

In Pari-GP scripts, = is an assignment operator. Thus "a = 1" assigns the value 1 to the variable "a".

But "==" is a comparison, result either TRUE (1) or FALSE (0). For example, the comparison...
Forum: Lounge 2022-09-08, 19:22
Replies: 16
Views: 208
Posted By Dr Sardonicus
I still remember seeing the video of a very young...

I still remember seeing the video of a very young Princess Elizabeth pledging to serve.- Princess Elizabeth on her 21st birthday (April 21, 1947).

Five years later she was Queen Elizabeth...
Forum: Soap Box 2022-09-08, 14:01
Replies: 14
Views: 1,119
Posted By Dr Sardonicus
I don't know about rapping, but maybe she's into...

I don't know about rapping, but maybe she's into break dancing. She can stand the notion of "Conservative" on its head with the best of them.

She has announced that the government is imposing...
Showing results 1 to 25 of 1000

 
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