Author:
ANDRICA DORIN, ,TURCAS GEORGE C.,
Abstract
"We present two Diophantine equations that arise from some new results in the theory of partitions with equal sums. We link these to the problem of finding rational points on some hyperelliptic curves and we solve the latter, assisted by computer algebra packages, using a p-adic method pioneered by Chabauty and Coleman."
Reference14 articles.
1. "[1] D. Andrica and O. Bagdasar, The Cauchy integral formula with applications to polynomials, partitions and sequences. Proceedings of the XVth Int. Conf. on Mathematics and its Applications, November 1-3, 2018, Romania, Editura Politehnica, Timi¸soara, 2019, 12-25."
2. "[2] D. Andrica and O. Bagdasar, On k-partitions of multisets with equal sums. Ramanujan J. 55 (2021), 2, 421-435."
3. "[3] D. Andrica and I. Tomescu, On an integer sequence related to a product of trigonometric functions and its combinatorial relevance. J. Integer Seq. 5 (2002), 2, Article 02.2.4."
4. "4] D. Andrica and G. T¸ urca¸s, An elliptic Diophantine equation from the study of partitions. Stud. Univ. Babe¸s-Bolyai Math. 64 (2019), 3, 349-356."
5. "[5] J.S. Balakrishnan, F. Bianchi, V. Cantoral-Farf'an, M. C¸ iperiani, and A. Etropolski, Chabauty-Coleman experiments for genus 3 hyperelliptic curves. In: J.S. Balakrishnan et al. (Eds.), Research Directions in Number Theory, Women in numbers IV. Assoc. Women Math. Ser. 19, Springer, 2019, 67-90."