Representing integers as linear combinations of powers
نویسندگان
چکیده
منابع مشابه
Representing integers as linear combinations of powers
At a conference in Debrecen in October 2010 Nathanson announced some results concerning the arithmetic diameters of certain sets. (See his paper in the present volume.) He proposed some related problems on the representation of integers by sums or differences of powers of 2 and of 3. In this note we prove some results on this problem and the more general problem about the representation by line...
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A general framework based on linear algebra is presented to obtain old and new polynomial expressions for the sums of powers of integers. This framework uses changes of polynomial basis, infinite lower triangular matrices and finite differences.
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ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2011
ISSN: 0033-3883
DOI: 10.5486/pmd.2011.5132