Intercity Number Theory Seminar

Special day on the ABC-conjecture, September 9 2005

This is the kick-off meeting of an NWO sponsored "Leraar in Onderzoek" project that will help Kennislink to take ABC to the masses.

September 9 Leiden, room 412.
11:15-12:00Frits Beukers (Utrecht), Introduction to the ABC conjecture [PDF]
12:15-12:45Jaap Top (Groningen), Finding good ABC triples, part I; notes in Dutch (PDF)
14:00-14:30Johan Bosman (Leiden), Finding good ABC triples, part II; notes in Dutch (PDF)
14:45-15:30Hendrik Lenstra (Leiden), Granville's theorem; notes in Dutch (PDF)
Abstract. Barry Mazur defined the `power' of a number to be the logarithm of the number to the base its radical. For example, every perfect square has power at least 2. How many integers up to a large bound have power at least a given number? This question is answered by Granville's theorem. It is of importance both in understanding why the ABC-conjecture has a chance of being true, and in analyzing an algorithm for enumerating ABC-triples.
15:45-16:15Willem Jan Palenstijn (Leiden), Enumerating ABC triples; notes in Dutch (PDF)
Abstract. An ABC triple is a triple of coprime positive integers a, b, c with a + b = c and c larger than the radical of abc. In this talk we present an algorithm that enumerates all ABC triples with c smaller than a given upper bound N with a runtime essentially linear in N.
16:30-17:00Carl Koppeschaar (Kennislink), Reken mee met ABC [PPT]