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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.
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September 9 |
Leiden, room 412.
| | 11:15-12:00 | Frits Beukers (Utrecht), Introduction to the
ABC conjecture
[PDF]
| | 12:15-12:45 | Jaap Top (Groningen), Finding good ABC triples,
part I; notes in Dutch (PDF)
| | 12:45-14:00 | Lunch
| 14:00-14:30 | Johan Bosman (Leiden), Finding good ABC
triples, part II;
notes in Dutch (PDF)
| | 14:45-15:30 | Hendrik 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.
| | 15:45-16:15 | Willem 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.
| | 16:30-17:00 | Carl Koppeschaar (Kennislink), Reken mee met
ABC
[PPT]
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