4 papers
Sums of four and more unit fractions and approximate parametrizations
Christian Elsholtz, Stefan Planitzer
We prove new upper bounds on the number of representations of rational numbers as a sum of unit fractions, giving five different regions, depending on the size of…
The number of solutions of the Erdős-Straus Equation and sums of unit fractions
Christian Elsholtz, Stefan Planitzer
We prove new upper bounds for the number of representations of an arbitrary rational number as a sum of three unit fractions. In particular, for fixed there are at most $\mathc…
On Erdős and Sárközy's sequences with Property P
Christian Elsholtz, Stefan Planitzer
A sequence of positive integers having the property that no element divides the sum of two larger elements is said to have `Property P'. We construct an i…
Romanov's Theorem in Number Fields
Manfred G. Madritsch, Stefan Planitzer
Romanov proved that a positive proportion of the integers have a representation as a sum of a prime and a power of an arbitrary fixed positive integer. Rieger proved the analogous…