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Trygve Nagell
Trygve Nagell or Trygve Nagel (July 13, 1895 in Oslo – January 24, 1988 in Uppsala) was a Norwegian mathematician, known for his works on Diophantine equations in number theory. Education and career He was born Nagel and adopted the spelling Nagell later in life. He received his doctorate at the University of Oslo in 1926, where his advisor was Axel Thue. He continued to lecture at the University until 1931. He was a professor at the University of Uppsala from 1931 to 1962. His doctoral students include Harald Bergström. Contributions Nagell proved a conjecture of Srinivasa Ramanujan that there are only five numbers that are both triangular numbers and Mersenne numbers. They are the numbers 0, 1, 3, 15, and 4095. The formula expressing the equality of a triangular number and a Mersenne number can be simplified to the equivalent form :2^n-7=x^2, which likewise has five solutions in natural numbers n and x, with solutions for n \in\. In honor of Nagell's solution, this ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramanujan–Nagell Equation
In mathematics, in the field of number theory, the Ramanujan–Nagell equation is an equation between a square number and a number that is seven less than a power of two. It is an example of an exponential Diophantine equation, an equation to be solved in integers where one of the variables appears as an exponent. The equation is named after Srinivasa Ramanujan, who conjectured that it has only five integer solutions, and after Trygve Nagell, who proved the conjecture. It implies non-existence of perfect binary codes with the minimum Hamming distance 5 or 6. Equation and solution The equation is :2^n-7=x^2 \, and solutions in natural numbers ''n'' and ''x'' exist just when ''n'' = 3, 4, 5, 7 and 15 . This was conjectured in 1913 by Indian mathematician Srinivasa Ramanujan, proposed independently in 1943 by the Norwegian mathematician Wilhelm Ljunggren, and proved in 1948 by the Norwegian mathematician Trygve Nagell. The values of ''n'' correspond to the values of ''x'' a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1988 Deaths
File:1988 Events Collage.png, From left, clockwise: The oil platform Piper Alpha explodes and collapses in the North Sea, killing 165 workers; The USS Vincennes (CG-49) mistakenly shoots down Iran Air Flight 655; Australia celebrates its Bicentennial on January 26; The 1988 Summer Olympics are held in Seoul, South Korea; Soviet troops begin their withdrawal from Afghanistan, which is completed the next year; The 1988 Armenian earthquake kills between 25,000-50,000 people; The 8888 Uprising in Myanmar, led by students, protests the Burma Socialist Programme Party; A bomb explodes on Pan Am Flight 103, causing the plane to crash down on the town of Lockerbie, Scotland- the event kills 270 people., 300x300px, thumb rect 0 0 200 200 Piper Alpha rect 200 0 400 200 Iran Air Flight 655 rect 400 0 600 200 Australian Bicentenary rect 0 200 300 400 Pan Am Flight 103 rect 300 200 600 400 1988 Summer Olympics rect 0 400 200 600 8888 Uprising rect 200 400 400 600 1988 Armenian ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1895 Births
Events January–March * January 5 – Dreyfus affair: French officer Alfred Dreyfus is stripped of his army rank, and sentenced to life imprisonment on Devil's Island. * January 12 – The National Trust for Places of Historic Interest or Natural Beauty is founded in England by Octavia Hill, Robert Hunter and Canon Hardwicke Rawnsley. * January 13 – First Italo-Ethiopian War: Battle of Coatit – Italian forces defeat the Ethiopians. * January 17 – Félix Faure is elected President of the French Republic, after the resignation of Jean Casimir-Perier. * February 9 – Mintonette, later known as volleyball, is created by William G. Morgan at Holyoke, Massachusetts. * February 11 – The lowest ever UK temperature of is recorded at Braemar, in Aberdeenshire. This record is equalled in 1982, and again in 1995. * February 14 – Oscar Wilde's last play, the comedy ''The Importance of Being Earnest'', is first shown at St James's The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of The Polar Star
The Royal Order of the Polar Star ( Swedish: ''Kungliga Nordstjärneorden'') is a Swedish order of chivalry created by King Frederick I on 23 February 1748, together with the Order of the Sword and the Order of the Seraphim. The Order of the Polar Star was until 1975 intended as a reward for Swedish and foreign "civic merits, for devotion to duty, for science, literary, learned and useful works and for new and beneficial institutions". Its motto is, as seen on the blue enameled centre of the badge, ''Nescit Occasum'', a Latin phrase meaning "It knows no decline". This is to represent that Sweden is as constant as a never setting star. The Order's colour is black. This was chosen so that when wearing the black sash, the white, blue and golden cross would stand out and shine as the light of enlightenment from the black surface. The choice of black for the Order's ribbon may also have been inspired by the black ribbon of the French Order of St. Michael, which at the time the O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Royal Norwegian Order Of St
Royal may refer to: People * Royal (name), a list of people with either the surname or given name * A member of a royal family Places United States * Royal, Arkansas, an unincorporated community * Royal, Illinois, a village * Royal, Iowa, a city * Royal, Missouri, an unincorporated community * Royal, Nebraska, a village * Royal, Franklin County, North Carolina, an unincorporated area * Royal, Utah, a ghost town * Royal, West Virginia, an unincorporated community * Royal Gorge, on the Arkansas River in Colorado * Royal Township (other) Elsewhere * Mount Royal, a hill in Montreal, Canada * Royal Canal, Dublin, Ireland * Royal National Park, New South Wales, Australia Arts, entertainment, and media * ''Royal'' (Jesse Royal album), a 2021 reggae album * ''The Royal'', a British medical drama television series * ''The Royal Magazine'', a monthly British literary magazine published between 1898 and 1939 * ''Royal'' (Indian magazine), a men's lifestyle bimonthly * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mathematical Intelligencer
''The Mathematical Intelligencer'' is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals. Volumes are released quarterly with a subset of open access articles. Springer also cross-publishes some of the articles in ''Scientific American''. Karen Parshall and Sergei Tabachnikov are currently the co-editors-in-chief. History The journal was started informally in 1971 by Walter Kaufman-Buehler, Alice Peters and Klaus Peters. "Intelligencer" was chosen by Kaufman-Buehler as a word that would appear slightly old-fashioned. An exploration of mathematically themed stamps, written by Robin Wilson, became one of its earliest columns. In 1978, the founders appointed Bruce Chandler and Harold "Ed" Edwards Jr. to serve jointly in the role of editor-in-chief. Prior to 1978, articles of the ''Intelligencer'' were not contained in regular volumes and were sent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beppo Levi
Beppo Levi (14 May 1875 – 28 August 1961) was an Italian mathematician. He published high-level academic articles and books, not only on mathematics, but also on physics, history, philosophy, and pedagogy. Levi was a member of the Bologna Academy of Sciences and of the Accademia dei Lincei. Early years Beppo Levi was born on May 14, 1875, in Turin, Italy, and he was an older brother of Eugenio Elia Levi. He obtained his ''laurea'' in mathematics in 1896 at age 21 from the University of Turin under Corrado Segre. He was appointed an Assistant Professor at the University of Turin three months later and shortly thereafter became a full-time Scholar. Levi was appointed Professor at the University of Piacenza in 1901, at the University of Cagliari in 1906, at the University of Parma in 1910, and finally at the University of Bologna in 1928. The years that followed his last appointment saw the rise of Benito Mussolini's power and of antisemitism in Italy, and Levi, being Je ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsion Conjecture
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of elliptic curves. Elliptic curves From 1906 to 1911, Beppo Levi published a series of papers investigating the possible finite orders of points on elliptic curves over the rationals. He showed that there are infinitely many elliptic curves over the rationals with the following torsion groups: * ''C''''n'' with 1 ≤ ''n'' ≤ 10, where ''C''''n'' denotes the cyclic group of order ''n''; * ''C''12; * ''C''2n × ''C''2 with 1 ≤ ''n'' ≤ 4, where × denotes the direct sum. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Élisabeth Lutz
Élisabeth Lutz (May 14, 1914 – July 31, 2008) was a French mathematician. The Nagell–Lutz theorem in Diophantine geometry describes the torsion points of elliptic curves; it is named after Lutz and Trygve Nagell, who both published it in the 1930s. Lutz was a student of André Weil at the University of Strasbourg, from 1934 to 1938. She earned a thesis for her research for him, on elliptic curves over p-adic fields. She completed her doctorate (''thèse d’état'') on p-adic Diophantine approximation at the University of Grenoble in 1951 under the supervision of Claude Chabauty; her dissertation was ''Sur les approximations diophantiennes linéaires p-adiques''. She became a professor of mathematics at the University of Grenoble The Université Grenoble Alpes (UGA, French: meaning "''Grenoble Alps University''") is a public research university in Grenoble, France. Founded in 1339, it is the third largest university in France with about 60,000 students and over 3,000 r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torsion (algebra)
In mathematics, specifically in ring theory, a torsion element is an element of a module that yields zero when multiplied by some non-zero-divisor of the ring. The torsion submodule of a module is the submodule formed by the torsion elements. A torsion module is a module that equals its torsion submodule. A module is torsion-free if its torsion submodule comprises only the zero element. This terminology is more commonly used for modules over a domain, that is, when the regular elements of the ring are all its nonzero elements. This terminology applies to abelian groups (with "module" and "submodule" replaced by "group" and "subgroup"). This is allowed by the fact that the abelian groups are the modules over the ring of integers (in fact, this is the origin of the terminology, that has been introduced for abelian groups before being generalized to modules). In the case of groups that are noncommutative, a ''torsion element'' is an element of finite order. Contrary to the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rational Number
In mathematics, a rational number is a number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator . For example, is a rational number, as is every integer (e.g. ). The set of all rational numbers, also referred to as "the rationals", the field of rationals or the field of rational numbers is usually denoted by boldface , or blackboard bold \mathbb. A rational number is a real number. The real numbers that are rational are those whose decimal expansion either terminates after a finite number of digits (example: ), or eventually begins to repeat the same finite sequence of digits over and over (example: ). This statement is true not only in base 10, but also in every other integer base, such as the binary and hexadecimal ones (see ). A real number that is not rational is called irrational. Irrational numbers include , , , and . Since the set of rational numbers is countable, and the set of real numbers is uncou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
