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Théophile Pépin
Jean François Théophile Pépin (14 May 1826 – 3 April 1904) was a French mathematician. Born in Cluses, Haute-Savoie, he became a Jesuit in 1846, and from 1850 to 1856 and from 1862 to 1871 he was Professor of Mathematics at various Jesuit colleges. He was appointed Professor of Canon Law in 1873, moving to Rome in 1880. He died in Lyon at the age of 77. His work centred on number theory. In 1876 he found a new proof of Fermat's Last Theorem for ''n'' = 7, and in 1880 he published the first general solution to Frénicle de Bessy's problem :''x''2 + ''y''2 = ''z''2, ''x''2 = ''u''2 + ''v''2, ''x'' − ''y'' = ''u'' − ''v''. He also gave his name to Pépin's test, a test of primality for Fermat number In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cluses
Cluses (; frp, Clluses) is a commune in the Haute-Savoie department in the Auvergne-Rhône-Alpes region in southeastern France. Citizens are known as ''Clusiens''. The commune is situated in the Arve Valley, on the river which bears the same name. Cluses is known for its Alpine setting and (during the first part of the 20th century) its watch-making industry. Geography The town is located in the Arve Valley, in the region Faucigny. Situated between Geneva and Chamonix, Cluses is located near a number of popular ski slopes. Population History During the Roman era, a bridge, was built across the Arve River. Travelers crossing the bridge soon stimulated trade in the area, and the first village was born at the center of the "cluse" (a narrow valley), situated between the mountains and the Arve River. Cluses became an independent commune on 4 May 1310. The Baron Hughes of Faucigny had an important role in the town's evolution as an independent commune. In 1720, Claude-Josep ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Haute-Savoie
Haute-Savoie (; Arpitan: ''Savouè d'Amont'' or ''Hiôta-Savouè''; en, Upper Savoy) or '; it, Alta Savoia. is a department in the Auvergne-Rhône-Alpes region of Southeastern France, bordering both Switzerland and Italy. Its prefecture is Annecy. To the north is Lake Geneva; to the south and southeast are Mont Blanc and the Aravis mountain range. It holds its name from the Savoy historical region, as does the department of Savoie, located south of Haute-Savoie. In 2019, it had a population of 826,094.Populations légales 2019: 74 Haute-Savoie INSEE Its subprefectures are [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jesuit
, image = Ihs-logo.svg , image_size = 175px , caption = ChristogramOfficial seal of the Jesuits , abbreviation = SJ , nickname = Jesuits , formation = , founders = , founding_location = , type = Order of clerics regular of pontifical right (for men) , headquarters = Generalate:Borgo S. Spirito 4, 00195 Roma-Prati, Italy , coords = , region_served = Worldwide , num_members = 14,839 members (includes 10,721 priests) as of 2020 , leader_title = Motto , leader_name = la, Ad Majorem Dei GloriamEnglish: ''For the Greater Glory of God'' , leader_title2 = Superior General , leader_name2 = Fr. Arturo Sosa, SJ , leader_title3 = Patron saints , leader_name3 = , leader_title4 = Ministry , leader_name4 = Missionary, educational, literary works , main_organ = La Civiltà Cattolica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Canon Law
Canon law (from grc, κανών, , a 'straight measuring rod, ruler') is a set of ordinances and regulations made by ecclesiastical authority (church leadership) for the government of a Christian organization or church and its members. It is the internal ecclesiastical law, or operational policy, governing the Catholic Church (both the Latin Church and the Eastern Catholic Churches), the Eastern Orthodox and Oriental Orthodox churches, and the individual national churches within the Anglican Communion. The way that such church law is legislated, interpreted and at times adjudicated varies widely among these four bodies of churches. In all three traditions, a canon was originally a rule adopted by a church council; these canons formed the foundation of canon law. Etymology Greek / grc, κανών, Arabic / , Hebrew / , 'straight'; a rule, code, standard, or measure; the root meaning in all these languages is 'reed'; see also the Romance-language ancestors of the Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rome
, established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption = The territory of the ''comune'' (''Roma Capitale'', in red) inside the Metropolitan City of Rome (''Città Metropolitana di Roma'', in yellow). The white spot in the centre is Vatican City. , pushpin_map = Italy#Europe , pushpin_map_caption = Location within Italy##Location within Europe , pushpin_relief = yes , coordinates = , coor_pinpoint = , subdivision_type = Country , subdivision_name = Italy , subdivision_type2 = Region , subdivision_name2 = Lazio , subdivision_type3 = Metropolitan city , subdivision_name3 = Rome Capital , government_footnotes= , government_type = Strong Mayor–Council , leader_title2 = Legislature , leader_name2 = Capitoline Assemb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lyon
Lyon,, ; Occitan: ''Lion'', hist. ''Lionés'' also spelled in English as Lyons, is the third-largest city and second-largest metropolitan area of France. It is located at the confluence of the rivers Rhône and Saône, to the northwest of the French Alps, southeast of Paris, north of Marseille, southwest of Geneva, northeast of Saint-Étienne. The City of Lyon proper had a population of 522,969 in 2019 within its small municipal territory of , but together with its suburbs and exurbs the Lyon metropolitan area had a population of 2,280,845 that same year, the second most populated in France. Lyon and 58 suburban municipalities have formed since 2015 the Metropolis of Lyon, a directly elected metropolitan authority now in charge of most urban issues, with a population of 1,411,571 in 2019. Lyon is the prefecture of the Auvergne-Rhône-Alpes region and seat of the Departmental Council of Rhône (whose jurisdiction, however, no longer extends over the Metropolis of Lyo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."German original: "Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik." Number theorists study prime numbers as well as the properties of mathematical objects made out of integers (for example, rational numbers) or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory are often best understood through the study of Complex analysis, analytical objects (for example, the Riemann zeta function) that encode properties of the integers, primes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers , , and satisfy the equation for any integer value of greater than 2. The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of '' Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pépin's Test
In mathematics, Pépin's test is a primality test, which can be used to determine whether a Fermat number is prime. It is a variant of Proth's test. The test is named for a French mathematician, Théophile Pépin. Description of the test Let F_n=2^+1 be the ''n''th Fermat number. Pépin's test states that for ''n'' > 0, :F_n is prime if and only if 3^\equiv-1\pmod. The expression 3^ can be evaluated modulo F_n by repeated squaring. This makes the test a fast polynomial-time algorithm. However, Fermat numbers grow so rapidly that only a handful of Fermat numbers can be tested in a reasonable amount of time and space. Other bases may be used in place of 3. These bases are: :3, 5, 6, 7, 10, 12, 14, 20, 24, 27, 28, 39, 40, 41, 45, 48, 51, 54, 56, 63, 65, 75, 78, 80, 82, 85, 90, 91, 96, 102, 105, 108, 112, 119, 125, 126, 130, 147, 150, 156, 160, ... . The primes in the above sequence are called Elite primes, they are: :3, 5, 7, 41, 15361, 23041, 26881, 61441, 87041, 163841, 544001, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fermat Number
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form :F_ = 2^ + 1, where ''n'' is a non-negative integer. The first few Fermat numbers are: : 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... . If 2''k'' + 1 is prime and ''k'' > 0, then ''k'' must be a power of 2, so 2''k'' + 1 is a Fermat number; such primes are called Fermat primes. , the only known Fermat primes are ''F''0 = 3, ''F''1 = 5, ''F''2 = 17, ''F''3 = 257, and ''F''4 = 65537 ; heuristics suggest that there are no more. Basic properties The Fermat numbers satisfy the following recurrence relations: : F_ = (F_-1)^+1 : F_ = F_ \cdots F_ + 2 for ''n'' ≥ 1, : F_ = F_ + 2^F_ \cdots F_ : F_ = F_^2 - 2(F_-1)^2 for ''n'' ≥ 2. Each of these relations can be proved by mathematical induction. From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common integer factor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Footnotes
A note is a string of text placed at the bottom of a page in a book or document or at the end of a chapter, volume, or the whole text. The note can provide an author's comments on the main text or citations of a reference work in support of the text. Footnotes are notes at the foot of the page while endnotes are collected under a separate heading at the end of a chapter, volume, or entire work. Unlike footnotes, endnotes have the advantage of not affecting the layout of the main text, but may cause inconvenience to readers who have to move back and forth between the main text and the endnotes. In some editions of the Bible, notes are placed in a narrow column in the middle of each page between two columns of biblical text. Numbering and symbols In English, a footnote or endnote is normally flagged by a superscripted number immediately following that portion of the text the note references, each such footnote being numbered sequentially. Occasionally, a number between brack ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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