Infinite Sets of Integers Whose Distinct Elements Do Not Sum to a Power
Artūras Dubickas and Paulius Šarka
Department of Mathematics and Informatics
We first prove two results which both imply that for any sequence
of asymptotic density zero there exists an infinite sequence
such that the sum of any number of distinct elements of
does not belong to
Then, for any
we construct an
infinite sequence of positive integers
that no sum of some distinct elements of
is a perfect square.
Finally, given any finite set
we construct a
of the same growth, namely,
such that no sum of its distinct
elements is equal to
Full version: pdf,
Received November 13 2006;
revised version received December 4 2006.
Published in Journal of Integer Sequences December 4 2006.
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