“Lagrange's Four-Square Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Lagrange's Four-Square Theorem

释义

Lagrange's Four-Square Theorem

A theorem also known as Bachet's Conjecture which was stated but not proven by Diophantus. It states that everyPositive Integer can be written as the Sum of at most four Squares. Althoughthe theorem was proved by Fermat using infinite descent, the proof was suppressed. Euler was unableto prove the theorem. The first published proof was given by Lagrange in 1770 and made use of the EulerFour-Square Identity.

See also Euler Four-Square Identity, Fermat's Polygonal Number Theorem,Fifteen Theorem, Vinogradov's Theorem, Waring's Problem

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