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This theorem can be used to prove Lagrange's four-square theorem, which states that all natural numbers can be written as a sum of four squares. Gauss [ 10 ] pointed out that the four squares theorem follows easily from the fact that any positive integer that is 1 or 2 mod 4 is a sum of 3 squares, because any positive integer not divisible by 4 ...
Lickorish–Wallace theorem (3-manifolds) Lie's theorem (Lie algebra) Lie's third theorem ; Lie–Palais theorem (differential geometry) Lindemann–Weierstrass theorem (transcendental number theory) Lie–Kolchin theorem (algebraic groups, representation theory) Liénard's theorem (dynamical systems) Lindelöf's theorem (complex analysis)
Mahler's compactness theorem; Manin–Drinfeld theorem; Mann's theorem; Marsaglia's theorem; Matiyasevich's theorem; Mestre bound; Meyer's theorem; Midy's theorem; Mihăilescu's theorem; Minkowski's theorem; Modularity theorem; Multiplicity-one theorem
Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the n th triangular number. In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text.
The Geometry of Numbers is based on a book manuscript that Carl D. Olds, a New Zealand-born mathematician working in California at San Jose State University, was still writing when he died in 1979. Anneli Cahn Lax , the editor of the New Mathematical Library of the Mathematical Association of America , took up the task of editing it, but it ...
In 1796 Gauss proved his Eureka theorem that every positive integer n is the sum of 3 triangular numbers; this is trivially equivalent to the fact that 8n+3 is a sum of 3 squares. I would understand this sentence so that if one has a 3-triangular composition of n, we can determine a 3-square composition of 8n+3 and vice versa.
This book is divided into three parts: Part One An introduction to the principles on which Best Year Yet is based, as well as sharing the experiences of many people who have participated in the process over the years. Part Two Each of the 10 questions has its own chapter in which I review the background material and provide
A Treatise on the Binomial Theorem is a fictional work of mathematics by the young Professor James Moriarty, the criminal mastermind and archenemy of the detective Sherlock Holmes in the fiction of Arthur Conan Doyle. The actual title of the treatise is never given in the stories; Holmes simply refers to "a treatise upon the Binomial Theorem".