In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of...

In mathematics, the ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle...

number fields with class number 1. It is believed that there are infinitely many such number fields, but this has not been proven. The class number of...

polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer...

such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–)Stark–Heegner...

theory of binary quadratic forms. There remain some unsolved problems. The class number problem is particularly important. For a nonzero square free integer...

for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem. The Hardy–Littlewood conjecture F predicts...

In statistics, the reference class problem is the problem of deciding what class to use when calculating the probability applicable to a particular case...

complexity class #P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems associated with the decision problems in the...

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly...

rate of rk(N) (see Szemerédi's theorem) Class number problem: are there infinitely many real quadratic number fields with unique factorization? Fontaine–Mazur...

consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the...

special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed class number. Let Q denote the...

problem in computer science If the solution to a problem is easy to check for correctness, must the problem be easy to solve? More unsolved problems in...

Gaussian period Fermat's Last Theorem Class number problem for imaginary quadratic fields Stark–Heegner theorem Heegner number Langlands program Different ideal...

Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1. To simplify notation, let L {\displaystyle...

In number theory, the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function...

The #P-complete problems (pronounced "sharp P complete", "number P complete", or "hash P complete") form a complexity class in computational complexity...

of Baker's theorem contained such bounds, solving Gauss' class number problem for class number one in the process. This work won Baker the Fields medal...

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday...

complement problem. For example, one important problem is whether a number is a prime number. Its complement is to determine whether a number is a composite...

Boaz (Spring 2006). "Complexity of counting" (PDF). Princeton University. "counting problem". PlanetMath. "counting complexity class". PlanetMath. v t e...

Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers...

selected problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory...

whether a given rational number is a congruent number is called the congruent number problem. As of 2019[update], this problem has not been brought to...

algorithm to solve a single NP-hard problem would give polynomial time algorithms for all the problems in the complexity class NP. As it is suspected, but unproven...

Université de Montréal Gauss map in number theory Gaussian moat Gauss class number problem Gauss's multiplication formula Gaussian period Gaussian rational...

second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times...

the class NC (for "Nick's Class") is the set of decision problems decidable in polylogarithmic time on a parallel computer with a polynomial number of...

graph has a tour whose length is at most L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any...