A remark on prime (non)congruent numbers

TL;DR

This paper investigates prime numbers related to congruent numbers, focusing on primes of the form 8k+1, a case not fully addressed by previous research, to deepen understanding of their properties.

Contribution

It provides new insights into primes of the form 8k+1 concerning their status as congruent or non-congruent numbers, filling a gap in existing literature.

Findings

Identifies conditions under which primes of the form 8k+1 are congruent numbers.

Clarifies the status of primes of the form 8k+1 in the context of congruent number problem.

Extends previous results by addressing the previously unresolved case of primes p=8k+1.

Abstract

This paper discusses prime numbers that are (resp. are not) congruent numbers. Particularly the only case not fully covered by earlier results, namely primes of the form $p=8k+1$, receives attention.