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Search: Posts Made By: Dr Sardonicus
Forum: Lounge 2021-06-18, 15:47
Replies: 90
Poll: GIMPS shirts
Views: 23,829
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: 23,829
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: 187
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: 1,037
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: 235,280
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: 659
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: 6,760
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: 6,760
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: 39,862
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: 659
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: 14,310
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: 10,730
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: 659
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: 659
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: 39,862
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: 165,234
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: 220
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: 28,467
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: 152
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: 33,473
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: 1,575
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: 165,234
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: 340,408
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: 986
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...
Forum: Puzzles 2021-06-02, 23:39
Replies: 20
Views: 1,446
Posted By Dr Sardonicus
It's not clear to me what is allowed. Apparently...

It's not clear to me what is allowed. Apparently you are allowed to switch pairs, and keep track of which pairs you've switched. Given n envelopes and n letters, a given pairing-up of letters and...
Showing results 1 to 25 of 1000

 
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