Some studies on congruent numbers via the arithmetic of elliptic curves

Abstract

A congruent number is a positive integer that is the area of some right triangle with three rational number sides. In this thesis, we study the example of congruent numbers that are congruent to 5 (mod 8). To solve this problem, we analyze the relation between congruent numbers and elliptic curves. We change the congruent number problem to elliptic curve problem by Mordell's Theorem. we will provide an example which shows that all odd primes p<150 with p are congruent to 5 modulo 8.