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Search: Posts Made By: Dr Sardonicus
Forum: Math 2021-06-16, 15:56
Replies: 74
Views: 6,660
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: 6,660
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: 39,643
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: 8
Views: 486
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: 14,116
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: 10,527
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: 8
Views: 486
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: 8
Views: 486
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: 39,643
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: 1,736
RIP
Views: 164,504
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: 203
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: 28,282
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: 139
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: 33,235
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: 1,373
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: 1,736
RIP
Views: 164,504
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: 339,163
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: 961
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: 1,195
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...
Forum: Operation Billion Digits 2021-06-02, 02:46
Replies: 11
Views: 950
Posted By Dr Sardonicus
my what?? :w00t: Maybe yours![/QUOTE]:paul: Not...

my what?? :w00t:
Maybe yours![/QUOTE]:paul: Not "people." "Klingons!"
Forum: kriesel 2021-06-01, 14:02
Replies: 64
Views: 21,182
Posted By Dr Sardonicus
The worst passenger ship disaster in the US, the...

The worst passenger ship disaster in the US, the burning of the General Slocum on June 15, 1904, killed over a thousand people. The ship had been inspected and found "safe" a month earlier. ...
Forum: Operation Billion Digits 2021-06-01, 13:31
Replies: 11
Views: 950
Posted By Dr Sardonicus
There appears to be plenty of TF work available...

There appears to be plenty of TF work available seeking small factors of 2^p - 1 for p currently under consideration by GIMPS.

There is also plenty of work available to try to crack 2^p - 1 which...
Forum: Hardware 2021-05-31, 14:30
Replies: 60
Views: 3,107
Posted By Dr Sardonicus
Tangible forms of money - particularly precious...

Tangible forms of money - particularly precious metals - are reusable, and have the advantage that they obviate any question about whether the payer has it. Of course, they have the disadvantage...
Forum: Lone Mersenne Hunters 2021-05-30, 13:41
Replies: 1,892
Views: 236,207
Posted By Dr Sardonicus
Liar! Only 109 bits, 109.25 to be more exact....

Liar! Only 109 bits, 109.25 to be more exact. :razz:[/QUOTE]Oops.

From my "I can't count" liturgy:

Versicle: How many bits in two to the first power?

Responsory: Two, two.

Versicle: How...
Forum: Hobbies 2021-05-29, 12:36
Replies: 111
Views: 33,235
Posted By Dr Sardonicus
The ornamental Agave americana is commonly known...

The ornamental Agave americana is commonly known as the "century plant," although it usually only grows for 10-20 years before it flowers and dies.†

Fargesia nitida seems much more deserving of...
Showing results 1 to 25 of 1000

 
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