Journal ArticleDOI
The three-square theorem of Gauss and Legendre
TLDR
The following theorems are famous landmarks in the history of number theory: as discussed by the authors Theorem 1 (Fermat-Euler): A number is representable as a sum of two squares if, and only if, it has the form PQ2, where P is free of prime divisors.Abstract:
The following theorems are famous landmarks in the history of number theoryTheorem 1 (Fermat-Euler): A number is representable as a sum of two squares if, and only if, it has the form PQ2, where P is free of prime divisors q ≡ 3 (mod 4)Theorem 2 (Lagrange): Every number is representable as a sum of four squaresTheorem 3 (Gauss-Legendre): A number is representable as a sum of three squares if, and only if, it is not of the form 4a (8n + 7)read more
Citations
More filters
References
More filters
Book
A course in number theory
TL;DR: The central topics in number theory as taught in universities throughout the world are discussed in this paper, including divisibility and multiplicative functions, congruences and quadratic residues.
Journal ArticleDOI
Number theory: An approach through history; from Hammurapi to Legendre
TL;DR: This Number Theory: An Approach Through History; From Hammurapi To Legendre, as one of the most on the go sellers here will enormously be accompanied by the best options to review.
Journal ArticleDOI
André Weil: Number Theory: An approach through history. From Hammurapi to Legendre. Boston/Basel/Stuttgart: Birkhäuser 1983. XXI und 375 Seiten, Ln., DM 74,-.
Journal ArticleDOI
Sums of three squares
TL;DR: In this article, the authors make use of an elegant method of Professor H. Davenport [l] in the Geometry of Numbers to prove the Minkowski Theorem on lattice points contained within convex symmetric bodies.