n cannot be a congruent number. The proof of such a claim had to wait until Pierre de
Fermat. He showed that n = 1 and so every square number is not a congruent
number by using his method of infinite descent[6]. One can look at [4] and
[7] for Fermat’s descent method. In the present study we will show that if n
is a congruent number then n can not be a perfect square by using the same
method. Moreover, we proved Fermat’s last theorem for n = 4, which states
that the equation x4 + y4 = z4 has no solutions in positive integers.