Journal of Number Theory | 2019
Some new families of non-congruent numbers
Abstract
Abstract We construct several new families of non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8. Our results generalize the work of Reinholz, Spearman and Yang [14] . Our methods are based on Monsky s formula on the 2-Selmer rank of the congruent elliptic curve and the recent results by Tian, Yuan and Zhang on the congruent number problem.