Abstract
In this study, by showing that the systems of simultaneous equations
a2 − b2 = x2
and
a2 + b2 = y2
have no solutions in positive integers, we proved that a congruent number
can not be a perfect square. Moreover we proved Fermat’s last
theorem for n = 4.
Keywords: Congruent number, primitive Pythagorean triple, Fermat’s
last theorem