Büchi's problem, the Glossary

Table of Contents

1. 10 relations: Bombieri–Lang conjecture, Decidability (logic), First-order logic, Hilbert's tenth problem, Julius Richard Büchi, Number theory, Paul Vojta, Quadratic form, Saunders Mac Lane, Yuri Matiyasevich.

2. Squares in number theory

Bombieri–Lang conjecture

In arithmetic geometry, the Bombieri–Lang conjecture is an unsolved problem conjectured by Enrico Bombieri and Serge Lang about the Zariski density of the set of rational points of an algebraic variety of general type.

See Büchi's problem and Bombieri–Lang conjecture

Decidability (logic)

In logic, a true/false decision problem is decidable if there exists an effective method for deriving the correct answer.

See Büchi's problem and Decidability (logic)

First-order logic

First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.

See Büchi's problem and First-order logic

Hilbert's tenth problem

Hilbert's tenth problem is the tenth on the list of mathematical problems that the German mathematician David Hilbert posed in 1900.

See Büchi's problem and Hilbert's tenth problem

Julius Richard Büchi

Julius Richard Büchi (1924–1984) was a Swiss logician and mathematician.

See Büchi's problem and Julius Richard Büchi

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 functions.

See Büchi's problem and Number theory

Paul Vojta

Paul Alan Vojta (born September 30, 1957) is an American mathematician, known for his work in number theory on Diophantine geometry and Diophantine approximation.

See Büchi's problem and Paul Vojta

Quadratic form

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). Büchi's problem and quadratic form are quadratic forms and Squares in number theory.

See Büchi's problem and Quadratic form

Saunders Mac Lane

Saunders Mac Lane (August 4, 1909 – April 14, 2005), born Leslie Saunders MacLane, was an American mathematician who co-founded category theory with Samuel Eilenberg.

See Büchi's problem and Saunders Mac Lane

Yuri Matiyasevich

Yuri Vladimirovich Matiyasevich, (Ю́рий Влади́мирович Матиясе́вич; born 2 March 1947 in Leningrad) is a Russian mathematician and computer scientist.

See Büchi's problem and Yuri Matiyasevich

See also

Squares in number theory

• Büchi's problem
• Basel problem
• Brahmagupta–Fibonacci identity
• Brocard's conjecture
• Congruence of squares
• Congruum
• Degen's eight-square identity
• Dixon's factorization method
• Euler's criterion
• Euler's four-square identity
• Fermat's right triangle theorem
• Fermat's theorem on sums of two squares
• Gauss's lemma (number theory)
• History of the Theory of Numbers
• Integer triangle
• Jacobi's four-square theorem
• Lagrange's four-square theorem
• Legendre's conjecture
• Legendre's three-square theorem
• Olga Taussky-Todd
• Pythagorean prime
• Pythagorean quadruple
• Pythagorean triple
• Quadratic form
• Ramanujan's sum
• Ramanujan's ternary quadratic form
• Square (algebra)
• Square number
• Sum of squares function
• Sum of two squares theorem
• Sums of powers
• Sun Zhiwei
• The Book of Squares
• Triangular number
• Unit square
• Waring's problem
• Zolotarev's lemma

References

[1] https://en.wikipedia.org/wiki/Büchi's_problem