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1. The class number of a number field is the cardinality of the ideal class group of the field. 2. In group theory, the class number is the number of conjugacy classes of a group. 3. Class number is the number of equivalence classes of binary quadratic forms of a given discriminant. 4. The class number problem. conductor
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
Burton Spencer Dreben (September 27, 1927 – July 11, 1999) was an American philosopher specializing in mathematical logic. [1] A Harvard graduate who taught at his alma mater for most of his career (where he retired as Edgar Pierce Professor of Philosophy Emeritus), he published little but was a teacher and a critic of the work of his ...
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and David Masser in 1985. [ 1 ] [ 2 ] It is stated in terms of three positive integers a , b {\displaystyle a,b} and c {\displaystyle c} (hence the name) that are relatively prime and satisfy a ...
Six exponentials theorem (transcendental number theory) Skolem–Mahler–Lech theorem (number theory) Solutions to Pell's equation (number theory) Sophie Germain's theorem (number theory) Sphere packing theorems in dimensions 8 and 24 (geometry, modular forms) Stark–Heegner theorem (number theory) Subspace theorem (Diophantine approximation)
Traditionally, number theory is the branch of mathematics concerned with the properties of integers and many of its open problems are easily understood even by non-mathematicians. More generally, the field has come to be concerned with a wider class of problems that arise naturally from the study of integers.
Bernoulli number. Agoh–Giuga conjecture; Von Staudt–Clausen theorem; Dirichlet series; Euler product; Prime number theorem. Prime-counting function. Meissel–Lehmer algorithm; Offset logarithmic integral; Legendre's constant; Skewes' number; Bertrand's postulate. Proof of Bertrand's postulate; Proof that the sum of the reciprocals of the ...
Most recently, in 2020, Benjamin Burton classified all prime knots up to 19 crossings (of which there are almost 300 million). [4] [5] Starting with three crossings (the minimum for any nontrivial knot), the number of prime knots for each number of crossings is 1, 1, 2, 3, 7, 21, 49, 165, 552, 2176, 9988, 46972, 253293, 1388705, ...