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Variance of the root mean square value of the residuals of sine fitting in the presence of additive noise. [PDF]
Sci RepAlegria FAC.
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Handcuffed for 15 min: public perceptions of restraint and seclusion in schools: an experimental study of race and disability. [PDF]
Front PsycholTempleton D, Korchagin R.
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Canadian Journal of Mathematics, 1977
One of the nicest results in elementary number theory is the following, giving the relation between quadratic residues and sums of squares.
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One of the nicest results in elementary number theory is the following, giving the relation between quadratic residues and sums of squares.
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1998
Our main aim in this chapter is to determine which integers can be expressed as the sum of a given number of squares, that is, which have the form where each xi e ℤ, for a given k. We shall concentrate mainly on the two most important cases, characterising the sums of two squares, and showing that every non-negative integer is a sum of four squares. We
Gareth A. Jones, J. Mary Jones
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Our main aim in this chapter is to determine which integers can be expressed as the sum of a given number of squares, that is, which have the form where each xi e ℤ, for a given k. We shall concentrate mainly on the two most important cases, characterising the sums of two squares, and showing that every non-negative integer is a sum of four squares. We
Gareth A. Jones, J. Mary Jones
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SUMS OF SQUARES AND PARTITION CONGRUENCES
Journal of the Australian Mathematical Society, 2020AbstractFor positive integers $n$ and $k$, let $r_{k}(n)$ denote the number of representations of $n$ as a sum of $k$ squares, where representations with different orders and different signs are counted as distinct. For a given positive integer $m$, by means of some properties of binomial coefficients, we derive some infinite families of congruences ...
SU-PING CUI, NANCY S. S. GU
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Mathematische Zeitschrift, 2017
For any integer let s(K) be the smallest integer such that in any colouring of the set of squares of the integers in K colours every large enough integer can be written as a sum of no more than s(K) squares, all of the same colour. A problem proposed by Sarkozy asks for optimal bounds for s(K) in terms of K.
Prakash, Gyan +2 more
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For any integer let s(K) be the smallest integer such that in any colouring of the set of squares of the integers in K colours every large enough integer can be written as a sum of no more than s(K) squares, all of the same colour. A problem proposed by Sarkozy asks for optimal bounds for s(K) in terms of K.
Prakash, Gyan +2 more
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