Leiden University Student Repository

Horst, J.P. van der (2010)

Finding ABC-triples using Elliptic Curves

Master thesis | Mathematics (MSc)

When adding coprime numbers A and B, one could ask how big A, B, and A + B could be compared with the product of the prime numbers dividing these numbers. One can expect that this prime product has about three times as many digits as A + B, but with smart choices of A and B this prime product can be smaller than A + B. However, the so-called ABC-conjecture says that it cannot be much smaller. Several mathematicians have tried to develop algorithms creating infinitely many triples An, Bn, and An + Bn such that An + Bn is large compared to the product of the primes dividing one of the numbers An, Bn, and An + Bn. And I add a new algorithm to this list of algorithms and use the tool of elliptic curves, the zero set of a polynomial equation together with a group law, to create my triples.

Author

Horst, J.P. van der

Faculty

Faculty of Science

Supervisors

Smit, B. de

ECTS Credits

34

Language

en