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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
d8b3d5f31dd111f1e87d59f046e64029687d2644	both fermat's assertion and euler's conjecture were established	both fermat's assertion and euler's conjecture were established by joseph-louis lagrange. this more complicated formulation relies on the fact that o − 5 {\displaystyle {\mathcal {o}}_{\sqrt {-5}}} is not a principal ideal domain, unlike o − 2 {\displaystyle {\mathcal {o}}_{\sqrt {-2}}} and o − 3. {\displaystyle {\math...	wikipedia
361e00390d9a295cea7f058e211751219f1a0a6f	in a letter to blaise pascal dated september	in a letter to blaise pascal dated september 25, 1654 fermat announced the following two results that are essentially the special cases d = − 2 {\displaystyle d=-2} and d = − 3. {\displaystyle d=-3.} if p is an odd prime, then	wikipedia
ee494c370e2cf9ed697743d784083030ba746709	the above point of view on fermat's theorem	the above point of view on fermat's theorem is a special case of the theory of factorization of ideals in rings of quadratic integers. in summary, if o d {\displaystyle {\mathcal {o}}_{\sqrt {d}}} is the ring of algebraic integers in the quadratic field, then an odd prime number p, not dividing d, is either a prime ele...	wikipedia
029bf874d97d4fa8cb7ceabaafdd75368c6fcdc4	the multiplicative property of the norm implies that	the multiplicative property of the norm implies that a prime number p is either a gaussian prime or the norm of a gaussian prime. fermat's theorem asserts that the first case occurs when p = 4 k + 3, {\displaystyle p=4k+3,} and that the second case occurs when p = 4 k + 1 {\displaystyle p=4k+1} and p = 2. {\displaystyl...	wikipedia
27eebe87828619ce709520b6be01cd90c4ee8560	gaussian integers form a principal ideal domain. this	gaussian integers form a principal ideal domain. this implies that gaussian primes can be defined similarly as primes numbers, that is as those gaussian integers that are not the product of two non-units (here the units are 1, −1, i and − i).	wikipedia
038864330089e540bf865befd7c43cf822a25703	a gaussian integer is a complex number a	a gaussian integer is a complex number a + i b {\displaystyle a+ib} such that a and b are integers. the norm n (a + i b) = a 2 + b 2 {\displaystyle n(a+ib)=a^{2}+b^{2}} of a gaussian integer is an integer equal to the square of the absolute value of the gaussian integer. the norm of a product of gaussian integers is th...	wikipedia
7b967ff55146930ed1987e27bea4805cc43ab766	albert girard was the first to make the	albert girard was the first to make the observation, characterizing the positive integers (not necessarily primes) that are expressible as the sum of two squares of positive integers; this was published in 1625. the statement that every prime p of the form 4n+1 is the sum of two squares is sometimes called girard's the...	wikipedia
d7cbe395f1d7dd62ca97fa216ca4868183a2765b	since the diophantus identity implies that the product	since the diophantus identity implies that the product of two integers each of which can be written as the sum of two squares is itself expressible as the sum of two squares, by applying fermat's theorem to the prime factorization of any positive integer n, we see that if all the prime factors of n congruent to 3 modul...	wikipedia
6c42d2c14e6159f3fcd21c42e13ddfed5503fe7b	on the other hand, the primes 3, 7,	on the other hand, the primes 3, 7, 11, 19, 23 and 31 are all congruent to 3 modulo 4, and none of them can be expressed as the sum of two squares. this is the easier part of the theorem, and follows immediately from the observation that all squares are congruent to 0 (if number squared is even) or 1 (if number squared...	wikipedia
ec5118a10f88708c410e1b4aacf6e9c420048440	the prime numbers for which this is true	the prime numbers for which this is true are called pythagorean primes.for example, the primes 5, 13, 17, 29, 37 and 41 are all congruent to 1 modulo 4, and they can be expressed as sums of two squares in the following ways:	wikipedia
d86e09da984a255a06113005b2f5404a1c4e8fd9	while their findings were under peer review, the	while their findings were under peer review, the des moines register released a front-page article describing their findings (february 25, 2018). the researchers released a preprint of the article via the socarxiv within a day to ensure that detailed materials, methods, and interpretations of the data were fully availa...	wikipedia
22927dda820de1eb08e2fb8048797e4355bf800b	in 2016, lawrence-dill and sociologist shawn dorius began	in 2016, lawrence-dill and sociologist shawn dorius began work to better understand where negative public opinions on gmos and climate change originate. while investigating how gmos were portrayed in us news coverage, information on russian interference in the 2016 united states elections emerged, with english language...	wikipedia
877398bf3bd3fcd2420eba4d59760ee2b3fdad79	lawrence-dill regularly addresses timely topics like climate change	lawrence-dill regularly addresses timely topics like climate change and genetic engineering, advising colleagues to engage in discussions on these topics with colleagues in other disciplines, with policymakers, and with the general public. her guidance focuses on finding shared values, articulating social, environmenta...	wikipedia
cdb55289e492bb130b5bd7f58081928251cff46f	much of the work lawrence-dill has published seeks	much of the work lawrence-dill has published seeks to advance data sharing to enable researchers to make use of others' findings, as some scientists harbor concerns about data sharing that those who generate materials and data will not derive prominence from downstream use and benefits derived from their own data. howe...	wikipedia
2ac5bf8089c8d84bb5638243dc6a17931c9e1396	lawrence-dill has advanced plant scientists' ability to compute	lawrence-dill has advanced plant scientists' ability to compute on phenotype directly via connecting image-based phenotypes to genomics data, crowdsourcing for image-based machine learning, managing information for field and controlled environment high-throughput phenotyping, and computing on phenotypic descriptions.	wikipedia
0708b3e1e9c23ded3c213b326499df57821e1e13	lawrence-dill has advanced plant scientists' ability to access	lawrence-dill has advanced plant scientists' ability to access plant genomics resources by sequencing and assembling genomes, annotating structural elements including genes, regulatory elements and crispr sites to genomes, and creating tools that enable researchers to analyze gene expression data.	wikipedia
139b57631d64d886d7405fb1467b207eebaaab7b	lawrence-dill's research focuses on mapping genomes and gene	lawrence-dill's research focuses on mapping genomes and gene elements, predicting protein function, inventing new ways to link genes to phenotypic descriptions and images, developing ways to compute on phenotypic descriptions, organizing broad datasets for community access and use, and developing computational tools th...	wikipedia
6153d34991396ff1be8b17d63be015a664cb660e	in the summer of 2005, lawrence-dill began work	in the summer of 2005, lawrence-dill began work as a research geneticist for the usda-ars. she served as the director of maizegdb, the maize model organism database through december 2013. in 2014 she joined the faculty of iowa state university as an associate professor in the departments of genetics, development and ce...	wikipedia
c51acc3963fdedc501399a039e5f51eeee9cdd31	carolyn joy lawrence-dill, née cogburn, was born in	carolyn joy lawrence-dill, née cogburn, was born in el paso, texas. she grew up in throckmorton, then moved to cleburne in 1989. she graduated in 1992 from cleburne high school. lawrence-dill earned a b.a. degree in biology from hendrix college in 1996. she received her m.s. degree in biology in 1997 from texas tech un...	wikipedia
adec5e8377fbf4a5c434486ac6de7ff9e21bc82c	carolyn joy lawrence-dill (born may 18, 1974) is	carolyn joy lawrence-dill (born may 18, 1974) is an american plant biologist and academic administrator. she develops computational systems and tools to help plant science researchers use plant genetics and genomics data for basic biology applications that advance plant breeding.	wikipedia
277f25142295a83422226a20e6a54bf2b7f99a41	james donald martin was an american professional basketball	james donald martin was an american professional basketball player. he played for the basketball association of america's st. louis bombers and baltimore bullets between 1946 and 1949, averaging 3.0 points per game for his career. following his college career, martin obtained a master's degree from iowa state universit...	wikipedia
46d59edc32946895581a72edaf30506f7d33f50f	following his college career, martin obtained a master's	following his college career, martin obtained a master's degree from iowa state university. he then became a teacher and basketball coach, first at effingham high school, then at central junior high school in belleville, illinois, retiring in 1983.	wikipedia
4ba0ebfe0e06c9d30cfd3190c62267c3cc846dbd	james donald martin (february 7, 1920 – september	james donald martin (february 7, 1920 – september 30, 1997) was an american professional basketball player. he played for the basketball association of america 's st. louis bombers and baltimore bullets between 1946 and 1949, averaging 3.0 points per game for his career.	wikipedia
b2a667f07fae4548956b7172d40501ce5ec986d6	richard l. farley was an american professional basketball	richard l. farley was an american professional basketball player. a 6'4" swingman from winslow, indiana, farley played for the 1953 indiana university national championship team. he also played three seasons in the national basketball association as a member of the syracuse nationals and detroit pistons. he averaged 6....	wikipedia
9afceb3a59b2a2ab270981b89dafc031e2ca5fdf	farley previously held the nba record for the	farley previously held the nba record for the shortest amount of time on the floor before fouling out in a game, with five minutes' playing time, set on march 12, 1956. the record stood for 41 years until the dallas mavericks ' bubba wells broke it by getting himself disqualified in just 3 minutes on december 29, 1997.	wikipedia
8c05c9b04975f51efd4ef1b54b724dbf1636442b	a 6'4" (1.93 m) swingman from winslow, indiana,	a 6'4" (1.93 m) swingman from winslow, indiana, farley played for the 1953 indiana university national championship team. he also played three seasons (1954–1956; 1958–1959) in the national basketball association as a member of the syracuse nationals and detroit pistons. he averaged 6.5 points per game in his career an...	wikipedia
3b7f7aa03da6b3c274dd21d51b97bf2fbef77529	born in kragujevac, kočović had played for several	born in kragujevac, kočović had played for several clubs during his youth career before he joined vojvodina, where he spent the rest of youth career. he was licensed for the first team of the club in summer 2014, and was sitting on the bench in the 2nd leg match against trenčín in uefa europa league qualifications. he ...	wikipedia
987486412314384d82cbbdf3ed5113ff96762c57	nathan luke brattan is an australian professional football	nathan luke brattan is an australian professional football player who plays as a defensive midfielder for macarthur fc. born in england, brattan moved to australia at a young age, playing youth football for rochedale rovers and queensland lions before making his professional debut for brisbane roar. he spent several se...	wikipedia
1c86c19b3c7804cb4c4fddd0ce3135641b90f7f1	on 7 august 2018, during the first half	on 7 august 2018, during the first half of the first round match of 2018 ffa cup against brisbane roar brattan fell to the ground in a challenge with stefan mauk and was accidentally kicked in the head by the opposition player as mauk kicked the ball away. when the club doctor suspected he had suffered a spinal injury,...	wikipedia
8bbf3c481ac17384323311e41b65d05eb70c4867	in june 2016, brattan joined melbourne city on	in june 2016, brattan joined melbourne city on a one-year loan deal. he made his first appearance in a city shirt in a 5–0 friendly match win over port melbourne sc on 20 july 2016. on 1 august 2017, melbourne city announced that brattan's loan deal at the club had been extended for an additional year. on 5 july the cl...	wikipedia
f72dc63dc0765ccaa796617528ab159905312cb6	on the same day of signing for manchester	on the same day of signing for manchester city, he was immediately sent out on loan to bolton wanderers in the championship until 3 january 2016. however, the loan was cut short by two weeks and brattan was recalled by his parent club without having played a single game for bolton wanderers.	wikipedia
05dedc3ea452088de1cabae8b02f8d07329ddecb	following his release from brisbane roar, brattan was	following his release from brisbane roar, brattan was linked with a move to english premier league side manchester city. on 26 october 2015, brattan completed the free transfer move to manchester city on a four-year deal.	wikipedia
a150c37ec791dcda0602ce83f689723a0d6c4caa	brattan made his senior debut as a 19-year-old	brattan made his senior debut as a 19-year-old in the queensland roar 's "against racism" clash against the scottish football side celtic in 2009, displaying early potential. his debut a-league appearance was away to perth glory in december 2009. often described as one of the best passers of the ball at the club, bratt...	wikipedia
3bbb25ba7b970f8d6792a0216207da1bc8018be3	born in england, brattan moved to australia at	born in england, brattan moved to australia at a young age, playing youth football for rochedale rovers and queensland lions before making his professional debut for brisbane roar. he spent several seasons with the roar before leaving the club in 2015. he subsequently signed for manchester city, spending the majority o...	wikipedia
64a3a23538b6994df439ecd46baafbcc20beb967	the enzyme phosphoserine phosphatase catalyzes the reaction this	the enzyme phosphoserine phosphatase catalyzes the reaction this enzyme belongs to the family of hydrolases, specifically those acting on phosphoric monoester bonds. the systematic name is o-phosphoserine phosphohydrolase. this enzyme participates in glycine, serine and threonine metabolism.	wikipedia
1474a0cd8a40ef4b5cde5699bb0bd372b65d6de1	as of late 2007, 12 structures have been	as of late 2007, 12 structures have been solved for this class of enzymes, with pdb accession codes 1f5s, 1j97, 1l7m, 1l7n, 1l7o, 1l7p, 1l8l, 1l8o, 1nnl, 2j6y, 2j6z, and 2j70.	wikipedia
f73bdb6681acb98ca5b769e2c315f5bfc6a16ec2	this enzyme belongs to the family of hydrolases,	this enzyme belongs to the family of hydrolases, specifically those acting on phosphoric monoester bonds. the systematic name is o - phosphoserine phosphohydrolase. this enzyme participates in glycine, serine and threonine metabolism.	wikipedia
63020538745856b2223d20362122a668c8bb9f16	rhodobacter sphaeroides is a kind of purple bacterium;	rhodobacter sphaeroides is a kind of purple bacterium; a group of bacteria that can obtain energy through photosynthesis. its best growth conditions are anaerobic phototrophy (photoheterotrophic and photoautotrophic) and aerobic chemoheterotrophy in the absence of light. r. sphaeroides is also able to fix nitrogen. it ...	wikipedia
d9f23d7aa81e3509edd9dab5f1742925ca2b49b3	knowledge of the physiology of r. sphaeroides allowed	knowledge of the physiology of r. sphaeroides allowed the development of biotechnological processes for the production of some endogenous compounds. these are hydrogen, polyhydroxybutyrate and isoprenoids (e.g. coenzyme q10 and carotenoids). moreover, this microorganism is used also for wastewater treatment. hydrogen e...	wikipedia
b95c424ec2023698dd7bb75fe61d426802e77c5b	a genome-scale metabolic model exists for this microorganism,	a genome-scale metabolic model exists for this microorganism, which can be used for predicting the effect of gene manipulations on its metabolic fluxes. for facilitating genome editing in this species, a crispr/cas9 genome editing tool was developed and expanded. moreover, partitioning of intracellular fluxes has been ...	wikipedia