Combinatorical and Algebraic Structures Seminar

Date:	6.11.2012
Speaker:	Lajos Hajdu, Institute of Mathematics, University of Debrecen
Title:	Representation problems with units
Abstract:	In the talk we give a survey of results related to representation problems of different kinds with sums or linear combinations of units. As a starting point, we present a finiteness theorem concerning the length of arithmetic progressions in the set of $k$-term linear combinations of $S$-units. Then several related problems and applications are discussed, including the unit sum number problem and its generalizations, a problem of Peth\H{o} concerning arithmetic progressions in the solution sets of norm form equations and related results, a problem of Pohst about representing primes as $k$-term sums of $S$-integers and its generalizations, and a problem of Nathanson concerning the smallest integer not representable by $k$-term sums of $S$-integers. POZOR Seminář vyjímečně začíná v 12:30!

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