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 Showing results 1 to 25 of 1000 Search took 0.25 seconds. Search: Posts Made By: Dr Sardonicus
 Forum: Math 2021-04-14, 12:50 Replies: 8 Views: 4,650 Posted By Dr Sardonicus 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...
 Forum: Lounge 2021-04-13, 15:55 Replies: 1,348 Views: 110,978 Posted By Dr Sardonicus Given the rush to get shots in arms, having some... Given the rush to get shots in arms, having some inadequately trained vaccinators seems reasonably likely. Platelets are a major factor in forming blood clots, so it made me wonder how someone...
 Forum: Science & Technology 2021-04-13, 15:26 Replies: 46 Views: 10,582 Posted By Dr Sardonicus 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...
 Forum: Math 2021-04-13, 15:15 Replies: 8 Views: 4,650 Posted By Dr Sardonicus 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...
 2021-04-13, 14:06 Replies: 7 Views: 103 Posted By Dr Sardonicus Check. It's in the paper I linked to.Yes, but I... Check. It's in the paper I linked to.Yes, but I was being even more "flexible" than they were. :big grin: As a non-trivial example where normal and average orders both exist but are different: ...
 Forum: Lounge 2021-04-13, 13:17 Replies: 1,348 Views: 110,978 Posted By Dr Sardonicus 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...
 Forum: Lounge 2021-04-13, 12:44 Replies: 1,348 Views: 110,978 Posted By Dr Sardonicus Right on the head. Link to news story provided... Right on the head. Link to news story provided in this post (https://www.mersenneforum.org/showpost.php?p=575527&postcount=1338)
 2021-04-13, 12:15 Replies: 7 Views: 103 Posted By Dr Sardonicus 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)...
 Forum: Science & Technology 2021-04-12, 13:16 Replies: 46 Views: 10,582 Posted By Dr Sardonicus 'Huge' explosion rocks St. Vincent as volcano... 'Huge' explosion rocks St. Vincent as volcano keeps erupting (https://apnews.com/article/caribbean-coronavirus-pandemic-explosions-evacuations-2c26166fa05e0ec6840669972ea1aaf0)
 Forum: Science & Technology 2021-04-11, 17:57 Replies: 46 Views: 10,582 Posted By Dr Sardonicus More volcanic eruptions on Caribbean island of... More volcanic eruptions on Caribbean island of St. Vincent (https://apnews.com/article/caribbean-kingstown-volcanic-eruptions-79e3ee67522c30056ddeb5689c78ab82)
 Forum: Homework Help 2021-04-11, 15:59 Replies: 20 Views: 767 Posted By Dr Sardonicus 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...
 Forum: Lounge 2021-04-11, 14:58 Replies: 1,707 Views: 149,193 Posted By Dr Sardonicus Ramsey Clark... Ramsey Clark (https://apnews.com/article/politics-new-york-ron-kuby-slobodan-milosevic-lyndon-johnson-b7cd1d599e1d7ad7cc0a7152cabfc82c)
 Forum: Soap Box 2021-04-11, 13:17 Replies: 33 Views: 4,580 Posted By Dr Sardonicus From the "You'll have to read this to believe it,... From the "You'll have to read this to believe it, but you still won't believe it" department, is the following April 8, 2021 article in The Virginian-Pilot about a December 2020 traffic stop for DWB:...
 Forum: Miscellaneous Math 2021-04-10, 13:49 Replies: 35 Views: 652 Posted By Dr Sardonicus [The Colonel] Now I do my best to keep things... [The Colonel] Now I do my best to keep things moving along, but I'm not having things getting silly. [/The Colonel] Thread closed.
 Forum: Homework Help 2021-04-10, 12:47 Replies: 20 Views: 767 Posted By Dr Sardonicus Since OP number divides s^2 + 1 for s given by... Since OP number divides s^2 + 1 for s given by frmky, all factors are congruent to 1 (mod 4), hence congruent to 1 or 5 (mod 8). OP number is congruent to 1 (mod 8). Hence, evenly many of its...
 Forum: Lounge 2021-04-09, 01:32 Replies: 1,348 Views: 110,978 Posted By Dr Sardonicus One prediction coming from the "economy is more... One prediction coming from the "economy is more important than peoples' lives" crowd was that economic hardship from the public-health measures taken to mitigate the spread of COVID-19 would have...
 Forum: Miscellaneous Math 2021-04-09, 01:13 Replies: 35 Views: 652 Posted By Dr Sardonicus Ah, excellent! You've learned something: As a... Ah, excellent! You've learned something: As a definitive primality test, as Dr. McCoy might have said, "It's dead, Jim." You might also consider in future looking for counterexamples before...
 Forum: Lounge 2021-04-08, 16:06 Replies: 60 Views: 11,576 Posted By Dr Sardonicus I've seen more butterflies since March 21. ... I've seen more butterflies since March 21. Mostly the undesirable alien Pieris rapae, the European Cabbage Butterfly, but a couple of days ago a specimen of the Painted Lady Vanessa cardui, two Red...
 Forum: Miscellaneous Math 2021-04-08, 15:35 Replies: 35 Views: 652 Posted By Dr Sardonicus My bad, it's a fourth root of 1 when f == 1 (mod... My bad, it's a fourth root of 1 when f == 1 (mod 8) is prime. Computing a few examples indicates that when f is prime, f == 1 (mod 8), and the odd prime q = a^2 + b^2 is a quadratic non-residue...
 Forum: Miscellaneous Math 2021-04-07, 00:51 Replies: 35 Views: 652 Posted By Dr Sardonicus If f is prime and f == 7 (mod 8) , q is prime, q... If f is prime and f == 7 (mod 8) , q is prime, q == 1 (mod 4) and (q/f) = -1, let q = a^2 + b^2; a, b integers. Let R = Z, the ring of Gaussian integers. Then R/fR = GF(f^2), the field of f^2...
 Forum: Miscellaneous Math 2021-04-06, 13:21 Replies: 35 Views: 652 Posted By Dr Sardonicus It isn't what your paper says. It isn't what your paper says.
 Forum: Miscellaneous Math 2021-04-06, 13:02 Replies: 35 Views: 652 Posted By Dr Sardonicus 4 + 4*i = 1 + i (mod 7)??? :shock: 4 + 4*i = 1 + i (mod 7)??? :shock:
 Forum: Miscellaneous Math 2021-04-06, 12:43 Replies: 35 Views: 652 Posted By Dr Sardonicus f = 7 a = 1, b = 2, a^2 + b^2 = 5 5 is... f = 7 a = 1, b = 2, a^2 + b^2 = 5 5 is a quadratic non-residue (mod 7) exp = (7+1)/4 = 2 (1 + 2*i)^2 = -3 + 4*i =/= 1 + i (mod 7)
 Forum: Tales From the Crypt(o) 2021-04-05, 13:55 Replies: 280 Views: 66,548 Posted By Dr Sardonicus And yet people still provide all the data, for... And yet people still provide all the data, for free. :loco:[/QUOTE]This shouldn't be too surprising. Long before modern social media existed, people were going on national TV and telling millions of...
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