A note on congruent numbers

Abstract

An integer a is called a congruent number if and only if there are positive integer solutions to the system of equations \[ x 2 + a y 2 = z 2 and x 2 − a y 2 = t 2 . {x^2} + a{y^2} = {z^2}\quad {\text {and}}\quad {x^2} - a{y^2} = {t^2}. \] In this note congruent numbers are discussed and a table of known square-free congruent numbers less than 1000 is exhibited.