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Search: Posts Made By: Dr Sardonicus
Forum: sweety439 2021-06-24, 14:17
Replies: 369
Views: 23,503
Posted By Dr Sardonicus
I'm not sure why "E" is here used to denote...

I'm not sure why "E" is here used to denote decimal eleven - possibly because it's the first letter of the word "eleven?" In any case, it's gratuitously confusing. In the widely-used standard...
Forum: Lounge 2021-06-24, 11:44
Replies: 68
Views: 14,347
Posted By Dr Sardonicus
Western drought brings another woe: voracious...

Western drought brings another woe: voracious grasshoppers (https://apnews.com/article/droughts-science-government-and-politics-business-environment-and-nature-8c5863077b1e8f3876dd7d0b4426d27c)
Forum: Data 2021-06-24, 02:32
Replies: 34
Views: 603
Posted By Dr Sardonicus
Lemmings don't do that. ...

Lemmings don't do that. https://animals.howstuffworks.com/mammals/lemmings.htm
Lemmings don't commit mass suicide, Disney pushed them off a cliff...
Forum: Lounge 2021-06-23, 21:33
Replies: 1,740
RIP
Views: 165,670
Posted By Dr Sardonicus
Hmm, by committing suicide he may have avoided...

Hmm, by committing suicide he may have avoided being convicted of tax evasion, but the IRS will likely go after his money anyway.

The comedian Ernie Kovacs never paid his income taxes. After his...
Forum: Lounge 2021-06-23, 21:17
Replies: 229
Views: 40,124
Posted By Dr Sardonicus
As I was looking around my yard this morning, I...

As I was looking around my yard this morning, I found a dead rabbit by the street near my mailbox. The body looked largely intact, but it had been decapitated. I suspected human activity, but it...
Forum: Puzzles 2021-06-23, 01:14
Replies: 9
Views: 475
Posted By Dr Sardonicus
Apparently. The page with the challenge...

Apparently. The page with the challenge currently lists fifty-seven solvers who earned the bonus.
Forum: FactorDB 2021-06-22, 16:14
Replies: 1,627
Views: 158,888
Posted By Dr Sardonicus
Alas, this post...

Alas, this post (https://mersenneforum.org/showpost.php?p=581502&postcount=5) indicates he might be part of the problem...
Forum: Soap Box 2021-06-22, 15:07
Replies: 376
Views: 48,268
Posted By Dr Sardonicus
I'm a little confused by the price. A number of...

I'm a little confused by the price. A number of articles say their top of the line Tread+ is $4300, but Peloton introduced a "far more affordable" $2500 model.

Reviews say the thing is well-made,...
Forum: Lounge 2021-06-22, 13:11
Replies: 229
Views: 40,124
Posted By Dr Sardonicus
Thousands of eggs abandoned after a drone scares...

Thousands of eggs abandoned after a drone scares off nesting birds (https://www.washingtonpost.com/science/2021/06/07/drone-crash-abandoned-eggs/)
Forum: MattcAnderson 2021-06-21, 14:09
Replies: 14
Views: 456
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: 23,951
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: 23,951
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: 210
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: 23
Views: 1,220
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: 2,907
Views: 236,005
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: 771
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: 6,778
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: 6,778
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: 229
Views: 40,124
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: 771
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: 14,428
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: 10,830
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: 771
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: 771
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: 229
Views: 40,124
Posted By Dr Sardonicus
Perhaps the birds are just cleaning up after the...

Perhaps the birds are just cleaning up after the messy squirrels...
Showing results 1 to 25 of 1000

 
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