Sums of Squares of Linear Forms.

R. Baeza; D. Leep; M. O'Ryan

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Asymptotic formulae are provided for the number of representations of a natural number as the sum of four and of three squares that are pairwise coprime.

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Roger Clement Crocker (2008)

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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...

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Note to the Paper "A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)" (Bull. Polish Acad. Sci. Math. 61 (2013), 23-26)

A. Schinzel (2013)

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A Positive Definite Binary Quadratic Form as a Sum of Five Squares of Linear Forms (Completion of Mordell's Proof)

A. Schinzel (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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The paper completes an incomplete proof given by L. J. Mordell in 1930 of the following theorem: every positive definite classical binary quadratic form is the sum of five squares of linear forms with integral coefficients.

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Some results on magic squares based on generating magic vectors and R-C similar transformations

Xiaoyang Ma, Kai-tai Fang, Yu hui Deng (2017)

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In this paper we propose a new method, based on R-C similar transformation method, to study classification for the magic squares of order 5. The R-C similar transformation is defined by exchanging two rows and related two columns of a magic square. Many new results for classification of the magic squares of order 5 are obtained by the R-C similar transformation method. Relationships between basic forms and R-C similar magic squares are discussed. We also propose a so called GMV (generating...