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Lagrange's Theorem On The Minimal Set Of Squares

It will be demonstrated that there is a thin basis of order four of minimal cardinality #A(x) = O(x^.25). The current literature shows the existence of a thin basis of order four of cardinality #A(x) = O(x^(.25+ε), ε > 0, but speculates on the existence of a thin basis of order four of minimal cardinality.

preprint2011arXivOpen access
N. A. Carella
math.NT
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N. A. Carella

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