Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

Mittagsseminar Talk Information

Date and Time: Thursday, November 04, 2004, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Gyula Károlyi (Eötvös Lorand Univ.)

Squares in arithemtic progressions

According to an old conjecture of Rudin, there is an absolute constant C such that any nonconstant N-term arithmetic progression of integers contains at most C√N perfect squares. The best upper bound O(N2/3polylog N) has been obtained by Bombieri, Granville, and Pintz, employing heavy tools from algebraic geometry.

In this talk I will present a simple combinatorial argument that gives the upper bound O(√N log d), where d is the common difference of the progression.

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