## Abstract

A congruent number is a positive integer which can be represented as the area of a right triangle such that all of its side lengths are rational numbers. The problem determining whether a given number is congruent is usually studied by computing the Mordell-Weil rank of the corresponding elliptic curve. The Monsky matrix gives a way to compute efficiently the 2-Selmer rank, thereby gives an upper bound for the Mordell-Weil rank. In this paper, by using Monsky's matrix, we present new families of non-congruent numbers such that all of their odd prime factors are of the form 8k+3. Our result generalizes previous works of Reinholz–Spearman–Yang [12] and Cheng–Guo [3].

Original language | English |
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Pages (from-to) | 474-501 |

Number of pages | 28 |

Journal | Journal of Number Theory |

Volume | 238 |

DOIs | |

Publication status | Published - 2022 Sept |

### Bibliographical note

Publisher Copyright:© 2021 Elsevier Inc.

## All Science Journal Classification (ASJC) codes

- Algebra and Number Theory