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Search took 0.26 seconds. Search: Posts Made By: Dr Sardonicus
Forum: Miscellaneous Math 2021-04-10, 13:49
Replies: 35
Views: 577
Posted By Dr Sardonicus
[The Colonel] Now I do my best to keep things...

[The Colonel] Now I do my best to keep things moving along, but I'm not having things getting silly. [/The Colonel]

Thread closed.
Forum: Homework Help 2021-04-10, 12:47
Replies: 13
Views: 422
Posted By Dr Sardonicus
Since OP number divides s^2 + 1 for s given by...

Since OP number divides s^2 + 1 for s given by frmky, all factors are congruent to 1 (mod 4), hence congruent to 1 or 5 (mod 8). OP number is congruent to 1 (mod 8). Hence, evenly many of its...
Forum: Lounge 2021-04-09, 01:32
Replies: 1,339
Views: 109,220
Posted By Dr Sardonicus
One prediction coming from the "economy is more...

One prediction coming from the "economy is more important than peoples' lives" crowd was that economic hardship from the public-health measures taken to mitigate the spread of COVID-19 would have...
Forum: Miscellaneous Math 2021-04-09, 01:13
Replies: 35
Views: 577
Posted By Dr Sardonicus
Ah, excellent! You've learned something: As a...

Ah, excellent! You've learned something: As a definitive primality test, as Dr. McCoy might have said, "It's dead, Jim."

You might also consider in future looking for counterexamples before...
Forum: Lounge 2021-04-08, 16:06
Replies: 60
Views: 11,383
Posted By Dr Sardonicus
I've seen more butterflies since March 21. ...

I've seen more butterflies since March 21. Mostly the undesirable alien Pieris rapae, the European Cabbage Butterfly, but a couple of days ago a specimen of the Painted Lady Vanessa cardui, two Red...
Forum: Miscellaneous Math 2021-04-08, 15:35
Replies: 35
Views: 577
Posted By Dr Sardonicus
My bad, it's a fourth root of 1 when f == 1 (mod...

My bad, it's a fourth root of 1 when f == 1 (mod 8) is prime. Computing a few examples indicates that when

f is prime, f == 1 (mod 8), and the odd prime q = a^2 + b^2 is a quadratic non-residue...
Forum: Miscellaneous Math 2021-04-07, 00:51
Replies: 35
Views: 577
Posted By Dr Sardonicus
If f is prime and f == 7 (mod 8) , q is prime, q...

If f is prime and f == 7 (mod 8) , q is prime, q == 1 (mod 4) and (q/f) = -1, let q = a^2 + b^2; a, b integers.

Let R = Z, the ring of Gaussian integers. Then R/fR = GF(f^2), the field of f^2...
Forum: Miscellaneous Math 2021-04-06, 13:21
Replies: 35
Views: 577
Posted By Dr Sardonicus
It isn't what your paper says.

It isn't what your paper says.
Forum: Miscellaneous Math 2021-04-06, 13:02
Replies: 35
Views: 577
Posted By Dr Sardonicus
4 + 4*i = 1 + i (mod 7)??? :shock:

4 + 4*i = 1 + i (mod 7)??? :shock:
Forum: Miscellaneous Math 2021-04-06, 12:43
Replies: 35
Views: 577
Posted By Dr Sardonicus
f = 7 a = 1, b = 2, a^2 + b^2 = 5 5 is...

f = 7

a = 1, b = 2, a^2 + b^2 = 5

5 is a quadratic non-residue (mod 7)

exp = (7+1)/4 = 2

(1 + 2*i)^2 = -3 + 4*i =/= 1 + i (mod 7)
Forum: Tales From the Crypt(o) 2021-04-05, 13:55
Replies: 280
Views: 65,496
Posted By Dr Sardonicus
And yet people still provide all the data, for...

And yet people still provide all the data, for free. :loco:[/QUOTE]This shouldn't be too surprising. Long before modern social media existed, people were going on national TV and telling millions of...
Forum: Science & Technology 2021-04-05, 13:45
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
They schedule the weather where you live? I'm...

They schedule the weather where you live? I'm impressed! Where I live, they only try to forecast the weather, and the forecast for two days ahead is iffy.

If you can actually reschedule your shot...
Forum: Puzzles 2021-04-05, 13:22
Replies: 16
Views: 618
Posted By Dr Sardonicus
But it says (my emphasis)Perhaps they need a...

But it says (my emphasis)Perhaps they need a proofreader...

I was merely quibbling over the length of a "step." The number of "steps" any actual mechanical "wheel of fortune" could take in one...
Forum: YAFU 2021-04-05, 12:51
Replies: 11
Views: 290
Posted By Dr Sardonicus
If memory serves, for quadratic sieves the result...

If memory serves, for quadratic sieves the result you need here is that a homogeneous system of linear equations with more equations than variables automatically contains a linear dependency. (A...
Forum: Miscellaneous Math 2021-04-04, 14:23
Replies: 35
Views: 577
Posted By Dr Sardonicus
These are the red elements in the graphic: ...

These are the red elements in the graphic:
http://devalco.de/unit_circle/system_unit_circle.php
(I think this is a wonderful applet, programmed in php)[/QUOTE]
No algorithm is given, and the...
Forum: Puzzles 2021-04-04, 13:39
Replies: 16
Views: 618
Posted By Dr Sardonicus
I noticed that also. As to "steps," the problem...

I noticed that also. As to "steps," the problem says (my emphasis)I am unable to reconcile this usage of "steps" with the usage WRT "unwinnable sets."

I also noteThe phrase "a little less" is...
Forum: Miscellaneous Math 2021-04-04, 12:57
Replies: 35
Views: 577
Posted By Dr Sardonicus
"Choose" how, exactly?What is p? It is not...

"Choose" how, exactly?What is p? It is not previously defined.

Giving up...
Forum: Science & Technology 2021-04-02, 14:00
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
Soreness, especially around the injection site,...

Soreness, especially around the injection site, is common. The RN who gave me my first jab said to use the arm, which I did, "to tolerance." It worked out the stiffness and relieved the soreness. ...
Forum: ONeil 2021-04-02, 13:40
Replies: 86
Views: 3,061
Posted By Dr Sardonicus
I haven't seen anything to support the assertion...

I haven't seen anything to support the assertion that the vaccine would "weaken everyone's immune response." On the contrary, I have heard a number of instances in which (1) people had a stronger...
Forum: Science & Technology 2021-04-01, 18:41
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
Her being 102, I'm glad it was a mild case and...

Her being 102, I'm glad it was a mild case and she's recovered! This is the first case I have heard of where a fully-vaccinated person had COVID-19 with symptoms.

People living in nursing homes...
Forum: Lounge 2021-04-01, 15:33
Replies: 2
Views: 167
Posted By Dr Sardonicus
Looking at images of the spiral, it appears that...

Looking at images of the spiral, it appears that the binary is merely 1010100 repeated over and over.
Forum: Science & Technology 2021-04-01, 14:49
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
It doesn't? I suppose you're going to say it's...

It doesn't? I suppose you're going to say it's also different from the identical image here (https://mersenneforum.org/showpost.php?p=570284&postcount=64)...
Forum: Science & Technology 2021-04-01, 13:33
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
So, the vaccine creates a specific "challenge"...

So, the vaccine creates a specific "challenge" (the "spike protein" with the mRNA vaccines) and your immune system clearly recognizes it as foreign, and responds accordingly. No viral trickery or...
Forum: Lounge 2021-03-31, 16:51
Replies: 209
Views: 32,230
Posted By Dr Sardonicus
Google La gazza ladra. I have read that it was...

Google La gazza ladra. I have read that it was (loosely) based on a true story, but, in real life, the magpie's thievery was not discovered until after the person accused had already been executed.
Forum: Science & Technology 2021-03-31, 15:37
Replies: 188
Views: 8,934
Posted By Dr Sardonicus
He knows the vaccine he got didn't have virus. ...

He knows the vaccine he got didn't have virus.

The symptomatic immune response to the vaccine still seems notable. It seems that vaccinated (and presumably immunized) people who have subsequently...
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