Forum: Lounge
2021-04-18, 14:04
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Replies: 1,710
Views: 150,112
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Forum: Miscellaneous Math
2021-04-18, 13:31
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Replies: 13
Views: 269
Thank you for explaining what the program...
Thank you for explaining what the program actually does.
The usage of "quadratic residue" in the thread title is completely wrong. The residue a (mod n) is a quadratic residue if x^2 == a (mod n)...
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Forum: Soap Box
2021-04-17, 13:10
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Replies: 40
Views: 4,815
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Forum: Lounge
2021-04-17, 02:24
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Replies: 61
Views: 11,756
On Monday April 12, I saw my first large...
On Monday April 12, I saw my first large butterfly of the year, a Papilio glaucus - Eastern Tiger Swallowtail, a large yellow butterfly with black stripes on its wings.
Today (Friday April 16),...
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Forum: Lounge
2021-04-16, 01:36
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Replies: 4,278
Views: 320,144
Blindly following the laws of exponents, yes,...
Blindly following the laws of exponents, yes, repeatedly raising to the i power you get x, xi, x-1, x-i, x, ...
Unfortunately, the "laws of exponents" can go haywire when the exponents aren't real...
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Forum: Soap Box
2021-04-16, 01:21
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Replies: 40
Views: 4,815
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Forum: Soap Box
2021-04-15, 15:34
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Replies: 40
Views: 4,815
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Forum: Science & Technology
2021-04-15, 15:02
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Replies: 52
Views: 10,927
Ugh. That almost looks like enough to warrant...
Ugh. That almost looks like enough to warrant starting with a shovel. A grain scoop works pretty well for shoveling snow off a flat roof. Of course, snow you can just throw over the edge. I'm not...
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Forum: Math
2021-04-15, 14:55
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Replies: 10
Views: 4,851
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Forum: Lounge
2021-04-15, 14:08
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Replies: 1,710
Views: 150,112
I have more sympathy than some for Madoff's...
I have more sympathy than some for Madoff's victims. Most people aren't investment experts - that's why they rely on advisors. Assuming his victims had checked on Madoff's reputation and record...
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Forum: Lounge
2021-04-15, 13:13
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Replies: 4,278
Views: 320,144
Good one! There are two different sequences...
Good one! There are two different sequences here. The first one repeats five four terms cyclically, the second is the one that converges to the value indicated: ? z=I;for(i=1,20,print(i" "z);z=z^I)...
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Forum: Lounge
2021-04-14, 13:57
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Replies: 1,710
Views: 150,112
Bernie Madoff...
Bernie Madoff (https://apnews.com/article/bernie-madoff-dead-9d9bd8065708384e0bf0c840bd1ae711)
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Forum: Math
2021-04-14, 12:50
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Replies: 10
Views: 4,851
Since c = log(2)/log(10) is irrational, the...
Since c = log(2)/log(10) is irrational, the simple continued fraction (SCF) for c does not terminate. If pn/qn is a convergent fraction,
|c - pn/qn| < 1/qnqn+1 < 1/qn^2.
So this degree of...
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Forum: Lounge
2021-04-13, 15:55
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Replies: 1,348
Views: 112,174
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Forum: Science & Technology
2021-04-13, 15:26
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Replies: 52
Views: 10,927
IIRC, you collect rainwater. I'm guessing that...
IIRC, you collect rainwater. I'm guessing that having dust on the roofs would be bad for that. Of course, the weight of a lot of dust and ash would collapse the roof.
But geez, using up water to...
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Forum: Math
2021-04-13, 15:15
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Replies: 10
Views: 4,851
Think: When do two consecutive integers have...
Think: When do two consecutive integers have different numbers of decimal digits?
One thing you do have to be careful about is that the value of log(2)/log(10) is sufficienty accurate. With an...
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Forum: Number Theory Discussion Group
2021-04-13, 14:06
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Replies: 7
Views: 110
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Forum: Lounge
2021-04-13, 13:17
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Replies: 1,348
Views: 112,174
The Latest: US suggests 'pause' J&J shots over...
The Latest: US suggests 'pause' J&J shots over clot reports (https://apnews.com/article/world-news-europe-england-coronavirus-pandemic-united-nations-28008ef665003ebf11c981ed330c5370)I don't know how...
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Forum: Lounge
2021-04-13, 12:44
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Replies: 1,348
Views: 112,174
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Forum: Number Theory Discussion Group
2021-04-13, 12:15
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Replies: 7
Views: 110
The "normal order" and "average order" are not...
The "normal order" and "average order" are not necessarily the same. Number of distinct prime factors, sum of prime-power exponents, and the divisor function (number of positive integer divisors)...
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Forum: Science & Technology
2021-04-12, 13:16
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Replies: 52
Views: 10,927
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Forum: Science & Technology
2021-04-11, 17:57
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Replies: 52
Views: 10,927
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Forum: Homework Help
2021-04-11, 15:59
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Replies: 20
Views: 866
There's a trick to find the remainder mod 8...
There's a trick to find the remainder mod 8 that's so foolproof, it even works for me: just take the remainder mod 8 of the last 3 digits. In this case, the OP's number ends in 529, and 529 = 8*66...
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Forum: Lounge
2021-04-11, 14:58
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Replies: 1,710
Views: 150,112
Ramsey Clark...
Ramsey Clark (https://apnews.com/article/politics-new-york-ron-kuby-slobodan-milosevic-lyndon-johnson-b7cd1d599e1d7ad7cc0a7152cabfc82c)
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Forum: Soap Box
2021-04-11, 13:17
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Replies: 40
Views: 4,815
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