Torsion points on curves and common divisors of a^k-1 and b^k-1
| dc.creator | Ailon, Nir | |
| dc.creator | Rudnick, Zeev | |
| dc.date | 2002-02-12 | |
| dc.date | 2002-12-17 | |
| dc.date.accessioned | 2026-07-07T04:46:24Z | |
| dc.date.available | 2026-07-07T04:46:24Z | |
| dc.description | We study the behavior of the greatest common divisor of a^k-1 and b^k-1, where a,b are fixed integers or polynomials, and k varies. In the integer case, we conjecture that when a and b are multiplicatively independent and in addition a-1 and b-1 are coprime, then a^k-1 and b^k-1 are coprime infinitely often. In the polynomial case, we prove a strong version of this conjecture. To do this we use a result of Lang's on the finiteness of torsion points on algebraic curves. We also give a matrix analogue of these results, where for a unimodular matrix A, we look at the greatest common divisor of the elements of the matrix A^k-I. | |
| dc.description | Conjecture B and Theorem 3 extended to the case of matrices with arbitrary determinant. Replaced the proof of Theorem 2 with a simpler one | |
| dc.identifier | https://arxiv.org/abs/math/0202102 | |
| dc.identifier | http://arxiv.org/abs/math/0202102 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63314 | |
| dc.subject | Number Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 11D61 | |
| dc.title | Torsion points on curves and common divisors of a^k-1 and b^k-1 | |
| dc.type | text |