Representing integers as linear combinations of powers

2011/08/18 by Hajdu, Lajos, Tijdeman, Rob
#11D85 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1108.3737

Abstract

At a conference in Debrecen in October 2010 Nathanson announced some results concerning the arithmetic diameters of certain sets. He proposed some related results on the representation of integers by sums or differences of powers of 2 and 3. In this note we prove some results on this problem and the more general problem about the representation by linear combinations of powers of some fixed integers.

Related

• Representation by sums of unlike powers
• Conjectures involving a generalization of the sums of powers of integers
• Representations of integers as quotients of sums of distinct powers of three
• Sums and Differences of Three k-th Powers
• Integer Powers Expressed as Nested Sums of Lower Powers modulo 2, 3