of the

The Netherlands

SPEAKING ON

At

in Daly Science room 206

at 7:30 pm

The 14

^{th}century French Musicologist Philippe de Vitry defined aharmonic numberto be a positive integer that is not divisible by any prime number greater than 3. Thus, the first fifteen harmonic numbers are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48. He had a special interest in pairs of consecutive integers that are both harmonic, such as, 1,2, or 2,3, or 3,4, or 8,9. Can further examples be found? De Vitry submitted this question to the learned rabbi Gersonides, and it is to an exposition of Gersonides's ingenious answer that the first half of the present lecture is devoted. In the second half we turn from the past to the future, and discuss a far reaching but unproved generalization of Gersonides's result. It is called the "abc conjecture", and many mathemticians feel that it is the successor to Fermat's Last Theorem as the Holy Grail of modern number theory.

Hendrik W. Lenstra, Jr. was born in 1949 in the Netherlands. He received his Ph.D. in mathematics from the Universiteit van Amsterdam in 1977, and became a full professor there in 1978. He joined the UC Berkeley faculty in 1987. Since 1998 he has divided his time between Berkeley and the Universiteit Leiden in the Netherlands.

Lenstra is active in number theory and algebra. He is best known for introducing advanced tenhniques in the area of number-theoretic algorithms, such as the use of elliptic curves for finding prime factors of large integers. He has been a member of the Royal Dutch Academy of Science since 1984, and a fellow of the American Academy for Arts and Sciences since 1996. He is a recipient of the Fulkerson Prize of the American Mathematical Society and the Mathematical Programming Society (1985), and of the Spinoza Award of the Nederlanse Organisatie voor Wetenschappelijk Onderzoek (1998).

How to get to Santa Clara University:

101From US Highway 101, take the De La Cruz Boulevard/Santa Clara exi t and follow the signs to El Camino and the main campus entrance. 280From I-280, take I-880 north toward Oakland to the Alameda exit. Turn left onto The Alameda (which becomes El Camino Real) to the main campus entrance. 880From I-880, take the Alameda exit, travel north (The Alameda becomes El Camino Real) to the main campus entrance.

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