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Search took 0.33 seconds. Search: Posts Made By: Dr Sardonicus
Forum: Dobri 2022-08-11, 13:19
Replies: 40
Views: 4,197
Posted By Dr Sardonicus
For odd p we have (2^((p+1)/2))^2 == 2 (mod q)...

For odd p we have (2^((p+1)/2))^2 == 2 (mod q) for every prime factor q of 2^p - 1, so 2 is a quadratic residue (mod q). As is well known, this means that q == 1 or 7 (mod 8).

It is also well...
Forum: Other Mathematical Topics 2022-08-11, 12:22
Replies: 5
Views: 121
Posted By Dr Sardonicus
I'm afraid I'm pretty much drawing a blank on...

I'm afraid I'm pretty much drawing a blank on this one. However, I did notice a couple of minor things.

If the base b = p, a prime number, or p > 2 is prime and b = p^e or 2*p^e, the...
Forum: Miscellaneous Math 2022-08-10, 13:04
Replies: 10
Views: 756
Posted By Dr Sardonicus
My mistake. I apologize. It just happened...

My mistake. I apologize.

It just happened that your post started a new page, I read "I propose this thread again," and thought it was a new thread.

That'll teach me to do moderator things...
Forum: Soap Box 2022-08-10, 12:48
Replies: 51
Views: 4,322
Posted By Dr Sardonicus
It was not so many centuries ago that the...

It was not so many centuries ago that the monarchs of Europe ruled by "divine right" - kings and queens were appointed by God, and you did what they said, or else.

And that went for their...
Forum: Soap Box 2022-08-09, 14:34
Replies: 51
Views: 4,322
Posted By Dr Sardonicus
It seems that on Monday, August 8, 2022 the FBI...

It seems that on Monday, August 8, 2022 the FBI executed a search warrant at Mar-a-Lago, and seized boxes of documents.

The property owner's son indicated it had to do with the National Archives....
Forum: Soap Box 2022-08-09, 14:30
Replies: 51
Views: 4,322
Posted By Dr Sardonicus
No. I was merely observing that all the...

No. I was merely observing that all the political despots with personality cults in recent history I could think of offhand were not worthy of the idolatry they demanded.
Forum: Dobri 2022-08-09, 13:17
Replies: 40
Views: 4,197
Posted By Dr Sardonicus
Reread the explanatory post by charybdis. Also...

Reread the explanatory post by charybdis. Also note the result I mentioned about when 2 is a fourth power residue (mod q). The result you state is an easy consequence of your hypothesis and those...
Forum: Hobbies 2022-08-09, 12:28
Replies: 49
Views: 4,233
Posted By Dr Sardonicus
Fearsome creature, bwaaaahahahaha! Good one! ...

Fearsome creature, bwaaaahahahaha! Good one! Reminds me of the rabbit in Monty Python and the Holy Grail.

After drinking my bug-repellant-laden sweat, that little butterfly probably transformed...
Forum: Hobbies 2022-08-09, 02:07
Replies: 49
Views: 4,233
Posted By Dr Sardonicus
I had a large ash tree removed a few years ago. ...

I had a large ash tree removed a few years ago. The top of the stump was just under 4 feet in diameter. It was far enough from any structures that burning it out was an option. It tried sending up...
Forum: Lounge 2022-08-08, 23:13
Replies: 129
Views: 22,340
Posted By Dr Sardonicus
Re "NO CAT ZONE" pic: I think I can read the...

Re "NO CAT ZONE" pic: I think I can read the cat's mind: "My house, my rules."

I do recall that our paternal grandmother ("Nana") had something of an aversion to cats. She wasn't allergic IIRC,...
Forum: Lounge 2022-08-08, 19:13
Replies: 1,973
RIP
Views: 236,324
Posted By Dr Sardonicus
David McCullough...

David McCullough (https://apnews.com/article/david-mccullough-historian-dies-7abe5997da74f30b1eab11e36b308fe3)I received a copy of his book The Great Bridge about the building of the Brooklyn Bridge,...
Forum: Hobbies 2022-08-08, 17:40
Replies: 49
Views: 4,233
Posted By Dr Sardonicus
An asparagus picker is an implement about a foot...

An asparagus picker is an implement about a foot long, with a V-shaped notch at the business end. The inside of the V is sharpened. It is commonly used to cut out lawn weeds at or near ground...
Forum: Dobri 2022-08-08, 14:32
Replies: 40
Views: 4,197
Posted By Dr Sardonicus
Thank you very much for digging up a pertinent...

Thank you very much for digging up a pertinent reference on when 2 is an 8th power (mod q) when q is congruent to 1 (mod 8).

An even older result is the criterion for when 2 is a biquadratic...
Forum: Hobbies 2022-08-08, 13:32
Replies: 49
Views: 4,233
Posted By Dr Sardonicus
After a very dry late Spring and early Summer, a...

After a very dry late Spring and early Summer, a lot of my plants were stunted and struggling. But we got a much-needed soaking rain the second week of July, and recently got another good soaking. ...
Forum: Lounge 2022-08-06, 20:57
Replies: 909
Views: 114,941
Posted By Dr Sardonicus
.

.
Forum: Lounge 2022-08-06, 16:41
Replies: 444
Views: 74,898
Posted By Dr Sardonicus
And a good thing it is, too. Of course, even...

And a good thing it is, too. Of course, even with your company, you have indicated that callers can go ahead and enter an extension if they know it.

I am generally resigned to having to deal with...
Forum: Soap Box 2022-08-05, 12:34
Replies: 54
Views: 13,694
Posted By Dr Sardonicus
This is a followup to previous posts about a...

This is a followup to previous posts about a notorious police shooting, e.g. this one (https://www.mersenneforum.org/showpost.php?p=557746&postcount=41) and this one...
Forum: Soap Box 2022-08-05, 02:46
Replies: 189
Views: 44,084
Posted By Dr Sardonicus
I made a mistake in my previous post. Jones's...

I made a mistake in my previous post. Jones's defense lawyer requested that the jury award not $1.00, but $1.00 for each of the eight counts in the suit, for a grand total of $8.00.

The jury has...
Forum: Lounge 2022-08-05, 00:05
Replies: 444
Views: 74,898
Posted By Dr Sardonicus
It's possible, but with the call I got, I think...

It's possible, but with the call I got, I think it's very unlikely.

Right off the bat, the number the call came from was "unavailable" to Caller ID. A legitimate business (which the call back...
Forum: Soap Box 2022-08-04, 20:37
Replies: 390
Views: 19,669
Posted By Dr Sardonicus
Dear Josh: Thanks for thinking of me. I...

Dear Josh:

Thanks for thinking of me.

I thought the last candidate I supported was going to run again.

And I thought you supported him as well.

Do you know something I don't?
Forum: Soap Box 2022-08-04, 13:01
Replies: 390
Views: 19,669
Posted By Dr Sardonicus
The US Senate has voted 95-1 to let Finland and...

The US Senate has voted 95-1 to let Finland and Sweden join NATO.

It is possible that objections from Turkey could still prevent them from joining - member states have to be unanimous in allowing...
Forum: And now for something completely different 2022-08-04, 11:50
Replies: 49
Views: 10,622
Posted By Dr Sardonicus
And there is a grand total of how many known...

And there is a grand total of how many known terms? Eleven.

But - the index suddenly jumps from 2732 to 19439060 - surely there must be something going on! Argle bargle! Argle bargle!
...
Forum: Lounge 2022-08-04, 02:33
Replies: 444
Views: 74,898
Posted By Dr Sardonicus
I got a really weird call to my cell phone on 2...

I got a really weird call to my cell phone on 2 August 2022. Caller ID said "unavailable," which told me right away it was some kind of scam. I let it go to voice mail.

And lo and behold, not...
Forum: Soap Box 2022-08-04, 01:57
Replies: 189
Views: 44,084
Posted By Dr Sardonicus
Here is a followup to this 2020 post...

Here is a followup to this 2020 post (https://www.mersenneforum.org/showpost.php?p=534064&postcount=135) about the Texas lawsuit against Alex Jones filed by parents of victims of the Sandy Hook...
Forum: Science & Technology 2022-08-03, 13:44
Replies: 76
Views: 40,674
Posted By Dr Sardonicus
I presume "strong in the past" refers to...

I presume "strong in the past" refers to "inflation."

The "accelerating expansion" theory is currently fashionable due to work which was the subject of the 2011 Nobel Prize in Physics, which was...
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