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 Showing results 1 to 25 of 1000 Search took 0.26 seconds. Search: Posts Made By: Dr Sardonicus
 Forum: Lounge 2021-06-18, 15:47 Replies: 90 Poll: GIMPS shirts Views: 23,798 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: 23,798 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: 173 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: 19 Views: 1,024 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: 2,904 Views: 235,198 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...
 2021-06-17, 13:19 Replies: 10 Views: 634 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: 6,755 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: 6,755 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: 39,840 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...
 2021-06-15, 13:01 Replies: 10 Views: 634 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 Sticky: Poll: COVID vaccination wavefront Views: 14,297 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: 10,720 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.
 2021-06-12, 15:03 Replies: 10 Views: 634 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. ...
 2021-06-10, 12:43 Replies: 10 Views: 634 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: 39,840 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: 1,737 Views: 165,177 Posted By Dr Sardonicus Martha White... Martha White (https://apnews.com/article/louisiana-boycotts-2e8c4355a86f83bc65ec8fd963bcc017)
 2021-06-08, 11:48 Replies: 4 Views: 219 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: 28,451 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...
 2021-06-04, 14:08 Replies: 1 Views: 152 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: 33,451 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: 1,566 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: 1,737 Views: 165,177 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: 340,313 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: 985 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: 1,418 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...
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