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The fifteen theorem, and generalizations

Bhargava, Manjul (2001) The fifteen theorem, and generalizations. In: Robert J. Bumcrot Festschrift, 11 May 2001, Hofstra University.

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Abstract

The classical "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four squares; that is, the quadratic form a2 + b2 + c2 + d2 represents all (positive) integers. When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers.

Item Type:Conference or Workshop Item (Paper)
Additional Information:This paper was given at the Robert J. Bumcrot Festschrift on May 11, 2001
Uncontrolled Keywords:The classical "Four Squares Theorem" of Lagrange asserts that any positive integer can be expressed as the sum of four squares; that is, the quadratic form a2 + b2 + c2 + d2 represents all (positive) integers. When does a general quadratic form represent all integers? When does it represent all odd integers? When does it represent all primes? We show how all these questions turn out to have very simple and surprising answers.
Subjects:Q Science > Q Science (General)
Q Science > QA Mathematics
ID Code:24
Deposited By:Admin HofPrints
Deposited On:03 January 2006

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