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The thesis investigates various aspects of an extensive
number-theoreti-cal problem
first raised by SYLVESTER [30] in 1884:
Given a set
of relatively prime
positive integers, which positive integers can be represented as
, where are non-negative integers.
In Chapter 2 we introduce the notions and show the
possibility of applications at school through a sequence of exercices.
In Chapter 3, after presenting results on the greatest non-representable number
and on the corresponding extremal version, our main result is a
generalization of a theorem by ERDŐS and GRAHAM
from 1972.
In Chapter 4 we summarize the results on the number of the
non-representable integers and we give
a complete solution of the corresponding extremal problem.
The last chapter deals with the sum of powers of
the non-representable integers.

root
2004-12-04