Journal of the Korean Mathematical Society (대한수학회지)
- Volume 33 Issue 3
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- Pages.651-655
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- 1996
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- 0304-9914(pISSN)
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- 2234-3008(eISSN)
A LOWER BOUND FOR THE NUMBER OF SQUARES WHOSE SUM REPRESENTS INTEGRAL QUADRATIC FORMS
- Kim, Myung-Hwan (Department of Mathematics Seoul National University ) ;
- Oh, Byeong-Kweon (Department of Mathematics Seoul National University )
- Published : 1996.08.01
Abstract
Lagrange's famous Four Square Theorem [L] says that every positive integer can be represented by the sum of four squares. This marvelous theorem was generalized by Mordell [M1] and Ko [K1] as follows : every positive definite integral quadratic form of two, three, four, and five variables is represented by the sum of five, six, seven, and eight squares, respectively. And they tried to extend this to positive definite integral quadratic forms of six or more variables.