mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 1000
Search took 0.27 seconds.
Search: Posts Made By: Dr Sardonicus
Forum: MattcAnderson 2021-06-21, 14:09
Replies: 14
Views: 430
Posted By Dr Sardonicus
In Mathematical Snapshots by Hugo Steinhaus there...

In Mathematical Snapshots by Hugo Steinhaus there is a number called "mega." The notation is called "Steinhaus-Moser notation." The notation is, n in a triangle means n^n, n in a square is n in n...
Forum: Lounge 2021-06-18, 15:47
Replies: 90
Poll: GIMPS shirts
Views: 23,882
Posted By Dr Sardonicus
Your mind slipped a cog. It happens. "I was in a...

Your mind slipped a cog. It happens. "I was in a hurry" is a likely explanation. BTW I once heard a police officer say that "I was in a hurry" was the most common explanation from drivers he...
Forum: Lounge 2021-06-18, 13:06
Replies: 90
Poll: GIMPS shirts
Views: 23,882
Posted By Dr Sardonicus
:confused2: "Cabriolet?" EDIT: As my...

:confused2:

"Cabriolet?"

EDIT: As my blood caffeine approaches working levels, it occurs to me that you might have meant "carabiner."
Forum: MattcAnderson 2021-06-18, 12:57
Replies: 5
Views: 201
Posted By Dr Sardonicus
The Frobenius or coin problem...

The Frobenius or coin problem (https://mathworld.wolfram.com/CoinProblem.html) is tantalizing because it has a closed-form solution for two variables - if gcd(a,b) = 1 the largest non-representable...
Forum: Math 2021-06-18, 12:25
Replies: 19
Views: 1,063
Posted By Dr Sardonicus
Not quite what you're asking, but possibly...

Not quite what you're asking, but possibly related:

Hardy-Ramanujan Theorem (https://mathworld.wolfram.com/Hardy-RamanujanTheorem.html)

Erdős-Kac Theorem...
Forum: Science & Technology 2021-06-17, 15:16
Replies: 2,904
Views: 235,480
Posted By Dr Sardonicus
So, not actually very large then.Wot? :confused: ...

So, not actually very large then.Wot? :confused:

Our galaxy is ~100,000 light year wide. I'd consider that larger than "several hundred" light years.[/QUOTE]
This reminds me of the game...
Forum: Number Theory Discussion Group 2021-06-17, 13:19
Replies: 10
Views: 721
Posted By Dr Sardonicus
Let f > 1 be an odd integer. The set of Gaussian...

Let f > 1 be an odd integer. The set of Gaussian integers mod f,

Mod(a,f) + Mod(b,f)*I

for which

Mod(a^2 + b^2, f) = Mod(1, f)

forms a subgroup of the multiplicative group (Z[I]/f)* of...
Forum: Math 2021-06-16, 15:56
Replies: 74
Views: 6,767
Posted By Dr Sardonicus
What - you don't want a forum with a bunch of...

What - you don't want a forum with a bunch of threads, each consisting of a single post? :wink:
Forum: Math 2021-06-16, 12:24
Replies: 74
Views: 6,767
Posted By Dr Sardonicus
This thread...

This thread (https://www.mersenneforum.org/showthread.php?t=20587), last post in February 2016, is devoted to number theory textbooks. It might be amusing to check the resources in it for "link...
Forum: Lounge 2021-06-15, 13:30
Replies: 227
Views: 39,901
Posted By Dr Sardonicus
I have for some time been noticing that the...

I have for some time been noticing that the leaves on my sedum have been getting nibbled. It's been mainly upper leaves, and only slight nibbling. Rabbits sometimes nibble the edges of leaves...
Forum: Number Theory Discussion Group 2021-06-15, 13:01
Replies: 10
Views: 721
Posted By Dr Sardonicus
If f = q, a prime number, the number of solutions...

If f = q, a prime number, the number of solutions to x^2 + y^2 = 1 (mod q) may be counted as follows:

Note that 1 + (a/q) or 1 + kronecker(a,q) is 2 if a is a quadratic residue (mod q), 0 if a is...
Forum: Science & Technology 2021-06-12, 15:55
Replies: 227
Views: 14,363
Posted By Dr Sardonicus
I think this guy's yet-to-be-invented "universal...

I think this guy's yet-to-be-invented "universal vaccine" qualifies as "less effective."

Geert Vanden Bossche Stokes Fear of COVID-19 Vaccine To Promote His Own Flawed 'Solution'...
Forum: Soap Box 2021-06-12, 15:37
Replies: 78
Views: 10,766
Posted By Dr Sardonicus
IMO Intel is more likely to leave if/when their...

IMO Intel is more likely to leave if/when their tax parasitism incentive provisions become less attractive. For example, they're getting an 80% discount on their property taxes.
Forum: Number Theory Discussion Group 2021-06-12, 15:03
Replies: 10
Views: 721
Posted By Dr Sardonicus
No. In (1), a^2 + b^2 =/= 0 (mod f) is not...

No.

In (1), a^2 + b^2 =/= 0 (mod f) is not sufficient to insure that a^2 + b^2 has a multiplicative inverse (mod f).

I leave the determination of the appropriate condition as an exercise.
...
Forum: Number Theory Discussion Group 2021-06-10, 12:43
Replies: 10
Views: 721
Posted By Dr Sardonicus
As already observed, taking a^2 and b^2 congruent...

As already observed, taking a^2 and b^2 congruent to 0 and 1 (mod f) is always a solution. Thus [0, 1] or [0, f-1] always work.

If f has more than one prime factor, there will be other solutions...
Forum: Lounge 2021-06-10, 12:03
Replies: 227
Views: 39,901
Posted By Dr Sardonicus
Perhaps the birds are just cleaning up after the...

Perhaps the birds are just cleaning up after the messy squirrels...
Forum: Lounge 2021-06-09, 14:39
Replies: 1,737
RIP
Views: 165,353
Posted By Dr Sardonicus
Martha White...

Martha White (https://apnews.com/article/louisiana-boycotts-2e8c4355a86f83bc65ec8fd963bcc017)
Forum: And now for something completely different 2021-06-08, 11:48
Replies: 4
Views: 224
Posted By Dr Sardonicus
I see the OP has answered graciously. :tu: I...

I see the OP has answered graciously. :tu:

I would have been tempted to answer "Yes." :wink:

I point out If the attached file was supposed to prove that 10^n + 7 is composite for all other n,...
Forum: Lounge 2021-06-06, 12:47
Replies: 236
Views: 28,501
Posted By Dr Sardonicus
As some may know, Operation Overlord (better...

As some may know, Operation Overlord (better known as D-Day), commenced on June 6, 1944. One indication of Dwight Eisenhower's view of leadership was that he anticipated the possibility that the...
Forum: Number Theory Discussion Group 2021-06-04, 14:08
Replies: 1
Views: 158
Posted By Dr Sardonicus
(n^2 - b*n)/(2*n+k-b) may be rewritten as ...

(n^2 - b*n)/(2*n+k-b) may be rewritten as

n/2 - (b+k)/4 + (k^2 - b^2)/(8*n+4*k-4*b)

The only way to make the expression a fraction whose denominator remains bounded as n increases without...
Forum: Hobbies 2021-06-04, 13:36
Replies: 111
Views: 33,531
Posted By Dr Sardonicus
Those pictures are informative. I'm guessing...

Those pictures are informative.

I'm guessing those little ponds by the foundation are where plants were dug out.

I don't know how long those ponds persist, but if it's more than a week you...
Forum: Information & Answers 2021-06-04, 13:24
Replies: 34
Views: 1,610
Posted By Dr Sardonicus
Congratulations on finding a factor! ...

Congratulations on finding a factor!

According to the detailed status report for exponent 168713323 (https://www.mersenne.org/report_exponent/?exp_lo=168713323&exp_hi=&full=1), TF was working the...
Forum: Lounge 2021-06-04, 12:56
Replies: 1,737
RIP
Views: 165,353
Posted By Dr Sardonicus
F. Lee Bailey...

F. Lee Bailey (https://www.cnn.com/2021/06/03/us/f-lee-bailey-lawyer-dies/index.html)
Forum: Lounge 2021-06-04, 12:51
Replies: 4,317
Views: 340,619
Posted By Dr Sardonicus
They've tried. It's really, really iffy. It...

They've tried. It's really, really iffy. It tends to rot.
Forum: Miscellaneous Math 2021-06-03, 13:53
Replies: 30
Views: 991
Posted By Dr Sardonicus
Using Nick's excellent presentation (linked to...

Using Nick's excellent presentation (linked to above), the interested reader will have no trouble showing that for each positive integer n, in base ten there are exactly two n-digit idempotents...
Showing results 1 to 25 of 1000

 
All times are UTC. The time now is 12:55.

Tue Jun 22 12:55:50 UTC 2021 up 25 days, 10:43, 1 user, load averages: 0.85, 1.15, 1.34

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.