``if the area of a rational right triangle were a square, then there would also be a smaller one with the same property, and so on, which is impossible.''OK, that wasn't so helpful. Anyway, we did everything on Thursday except 2b, i.e., suppose that
Then
from which we obtain a smaller solution.
There are integers
with
such that
Since
is a perfect square we can write
either
,
or
,
for integers
.
Then
which yields a smaller solution to
Then
which yields a smaller solution to
William Stein 2006-07-07