This works with all perfect numbers 2 < sup > p − 1 </ sup >( 2 < sup > p </ sup >− 1 ) with odd prime p and, in fact, all numbers of the form 2 < sup > m − 1 </ sup >( 2 < sup > m </ sup >− 1 ) for odd integer ( not necessarily prime ) m.

This interpretation is flawed by the fact it relies on a very odd reading of " good a will " to mean " incorrect judgements " rather than the more intuitive " good intentions.

Baird Searles, in Asimov's Science Fiction ( April 1984 ), says " the book lies in the uneasy boundary between surrealism and fantasy, given an odd literary status by its masquerade as a book of fact ".

Although this may seem an odd layout, it is in fact logical.

If n is odd, then the semidirect product is in fact a direct product, and any orthogonal matrix can be produced by taking a rotation matrix and possibly negating all of its columns.

The even numbers form an ideal in the ring of integers, but the odd numbers do not — this is clear from the fact that the identity element for addition, zero, is an element of the even numbers only.

Some scholars have proposed that the author took the list from a now-lost Old Welsh poem which listed Arthur's twelve great victories, based on the fact that some of the names appear to rhyme and the suggestion that the odd description of Arthur bearing the image of the Virgin Mary on his shoulders at Guinnion might contain a confusion of the Welsh word iscuit ( shield ) for iscuid ( shoulders ).

The frequency spectrum of the modulated color signal overlaps that of the baseband signal, and separation relies on the fact that frequency components of the baseband signal tend to be near harmonics of the horizontal scanning rate, while the color carrier is selected to be an odd multiple of half the horizontal scanning rate ; this produces a modulated color signal that consists mainly of harmonic frequencies that fall between the harmonics in the baseband luma signal, rather than both being in separate continuous frequency bands alongside each other in the frequency domain.

In the case that the algorithm returns " composite " because x = 1, it has also discovered that is ( an odd multiple of ) the order of a — a fact which can ( as in Shor's algorithm ) be used to factorize n, since n then divides but not either factor by itself.

Gauss's proof relies firstly on the fact that constructibility is equivalent to expressibility of the trigonometric functions of the common angle in terms of arithmetic operations and square root extractions, and secondly on his proof that this can be done if the odd prime factors of n are distinct Fermat primes, which are of the form.

In fact the difference will always be an odd multiple of q if q > 3.

The selection of six punctuation symbols may seem odd, but in fact the sixteen codes simply map to the ASCII range 0x30 through 0x3f, which defines ten digit characters plus those six symbols.

The notion of Mesklin's odd configuration stemmed from the fact that there were science fiction stories that featured low-gravity planets and high-gravity planets, but of course no single planet could have both low and high gravity.

Coupled with the fact that some programmers preferred louder more upbeat songs at the beginning and end of their program segments, caused them to cut odd sides outside in and even sides inside out, so that the tops and bottoms of hours would end on an upbeat note-as modern radio programmers do today.

The comments made by Ruri Hoshino in regards to the story and how the next episode will get back on track with it at the end of the episode along with the fact that the placing of the episode seems odd giving the events in the episodes before and after episode 14. seem to suggest the Nadesico episode being non-canon at the very least.

The name odd cycle transversal comes from the fact that a graph is bipartite if and only if it has no odd cycles.

From the period of the Jiajing Emperor ( 1522 – 66 ) on, a pair of phoenixes was differentiated by the tail feathers of the two birds ( typically together forming a closed circle pattern — the male identified by five serrated tail feathers ( five being an odd, or yang number ) and the female by what appears to be one, but is in fact, two ( two being an even, or yin number ) curling or tendrilled tail feathers.

" " Well, sometimes when people ask me that I have to think about whether or not I will answer because some people think it's an odd name even though I don't really because my mum gave it to me and I think my dad helped but it's as good a name as any in my opinion, I think it's a little weird to have the same name as two of my other names, but the fact that I like it is a good thing ... but yeah, it's Gordon.

The fact that by encircling the triangle an odd number of times, a line which originally may be seen as a positron, returns as an electron, is actually already a signature for the anomalous behavior of the diagram.

The original constitutional jurisdiction of the High Court is now well established: the Australian Law Reform Commission has described the inclusion of constitutional matters in section 76 rather than section 75 as " an odd fact of history.

But Åland was never to be granted the arms which was originally intended, instead it was awarded a coat of arms displaying a deer, an odd fact since the Åland fauna never included deer.

Penelope also has the odd habit of interjecting the word " please " into almost all of her sentences ( though in her website she puts this down to the fact that she has always been told to say " please " when she wants something, and she wants to meet Amanda ).

It follows from this theorem that all Carmichael numbers are odd, since any even composite number that is square-free ( and hence has only one prime factor of two ) will have at least one odd prime factor, and thus results in an even dividing an odd, a contradiction.

− 1 / 30, … are the Bernoulli numbers, and R is an error term which is normally small for suitable values of p and depends on n, m, p and f. ( The formula is often written with the subscript taking only even values, since the odd Bernoulli numbers are zero except for B < sub > 1 </ sub >.

* The Women's World Floorball Championships take place every December ( since 2009 ) in every odd year.

* The Men's under-19 World Floorball Championships take place every May ( since 2009 ) in every odd year.

His master may have agreed with his leaving since he offered the odd amount of 1 cent for his return and waited a month to post the notice in the local newspaper.

The order of a liquid crystal could also be characterized by using other even Legendre polynomials ( all the odd polynomials average to zero since the director can point in either of two antiparallel directions ).

Since p is prime q − 1 must be a multiple of p. Of course, if the number m = < sup >( q − 1 )</ sup >⁄< sub > p </ sub > is odd, then q will be even, since it is equal to mp + 1.

It's an odd accusation especially to those of us that practice Karaism, making no sense at all since there is no adherance to the Qur ' an and Mohammed is definitely not seen as a prophet.

This name, however, has not been in use since the 9th century, and it sounded quite odd to French people.

He said, " Everything in ' Cool ' [...] seems to exist in pastels and Bakshi shoots from more odd angles than any director since Sidney J. Furie in his heyday.

For example, 1 divided by 4 equals 1 / 4, which is neither even nor odd, since the concepts even and odd apply only to integers.

4x < sup > 2 </ sup > and 4x are even, which means that 4x < sup > 2 </ sup > + 4x + 1 is odd ( since even + odd = odd ).

The sample median may or may not be an order statistic, since there is a single middle value only when the number of observations is odd.

They have mentioned that if any one of them left then they would not continue since " it would really be strange to go on without one of the guys ," but they have emphasised that it would be an odd and unlikely situation since they work under the motivation that the five of them are " The Hives now, then and forever ".

For example, a = 3, b = 4, c = 6 is impossible since 3 + 4 + 6 = 13 is odd, and a = 3, b = 4, c = 9 is impossible since 3 + 4 < 9.

It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data with odd symmetry ( since the Fourier transform of a real and odd function is imaginary and odd ), where in some variants the input and / or output data are shifted by half a sample.

After she died, Young tried several jobs, and eventually moved in with friends John and Ruth Benedum and did odd jobs for them.

Unfortunately, in such calculations, Fermi did not take into account the " pairing energy " that might appear when a nuclide with an odd number of neutrons absorbed an extra neutron.

The idea of a solid that did not interact with other matter seemed a bit odd, and Augustin-Louis Cauchy suggested that perhaps there was some sort of " dragging ", or " entrainment ", but this made the aberration measurements difficult to understand.

As the original 68000 processor in Amigas tended only to access memory on every second available memory cycle, Agnus operated a system where the time-critical custom chips access got the " odd " clock cycle and the CPU got the " even " cycle, thus the CPU did not generally get locked out of memory access and did not appear to slow down.

Predating Goldberg, the corresponding term in the UK was, and still is, " Heath Robinson ", after the English illustrator with an equal devotion to odd machinery ( although Heath Robinson's creations did not have the same emphasis on the sequential or chain reaction element ).

As seen in later Deep Space Nine episodes, the Galaxy-class vessel was produced far in excess of its original run, so it does seem odd that the similarly advanced Keldon did not appear as often.

He visited St. Louis and did odd jobs in New York.

He dropped out in 1909 and worked as a farm labourer and did various odd jobs until he happened into acting.

After a few years, he left school with nothing more than a fourth grade English-language education and did odd jobs before being recruited to the army by a British colonial army officer.

He did odd jobs in the agricultural districts near Parramatta, driving a horse bus and hiring out on poultry farms.

During the 1990s, QuarkXPress steadily won ground from PageMaker, and it seemed increasingly odd that Adobe — who had created PostScript, so vital to the working of DTP — still did not offer its own page layout application.

In 1890 they moved to Balmain in Sydney, where he at first worked for Lewy Pattinson's pharmacy before he opened a small mixed shop, where he sold political pamphlets, did odd jobs and mended umbrellas.

Having begun his literary career, he did not return to NYU but rather took another series of odd jobs such as bank teller, mortuary assistant, and copy editor-all of which served to fuel what he referred to as his night-time " writing habit ".

At the time Gray's Inn was the odd one out amongst the Inns ; the others did not recognise Ancients as a degree of barrister and had Benchers roughly corresponding to the Readers used at Gray's Inn ( although the positions were not identical ).

Baburao Patel of Filmindia described Mother India after its release as " the greatest picture produced in India during forty and odd years of film-making " and later added that no other actress would have been able to perform the role as Nargis did.

In addition, it was hoped that programming quieter and more bass-heavy material at the center ( beginning of odd sides or ends of even sides ) would alleviate this problem, but it did not.

" To earn his keep he did various odd, but hard, jobs around the school.

Only after a short time did Henry Hallam notice the odd position of his head.

His tuition, $ 260 a year, exceeded his total earnings, and the workload prevented him from earning much money — though he did mow lawns and do odd jobs on weekends, and work at a cement factory in the summer.

In his early teens, he did farm chores and odd jobs for neighbors, too, saving his earnings.

The repairman knew his friend did not own a camper, and it would even strike Justice J. Raymond Paris at Reyat's 1991 trial as an odd use for a timer.

The usefulness of the ρ statistic can be seen in the case of the odd example used above, where two distributions that were significantly different on a U-test nonetheless had nearly identical medians: the ρ value in this case is approximately 0. 723 in favour of the hares, correctly reflecting the fact that even though the median tortoise beat the median hare, the hares collectively did better than the tortoises collectively.

He spent his life after high school doing odd jobs until he enlisted first in the United States Marine Corps and later the United States Navy during World War II, though he did not see any combat action due to the loss of vision in his right eye.