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)
Fermat’s method of "descente infinie" - Proof of Fermat’s Last Theorem for n=4
Stan Dolan
126A Harpenden Road, St. Albans
Introduction
Fermat proved the impossibility of finding positive in-
teger solutions of the equation x
4
+ y
4
= z
4
by a method
which he claimed would ’enable extraordinary develop-
ments to be made in the theory of numbers’ [1], His
method was based upon the idea of using a supposed
solution to find another solution, smaller than the first.
Proceeding in this fashion he could therefore obtain an
infinite series of smaller and smaller solutions. At this
point he concluded his proof as follows:
’This is, however, impossible because there cannot be
an infinite series of numbers [positive integers] smaller
than any given [positive] integer we please. The margin
is too small to enable me to give the proof completely and
with all details [1].’
The margin referred to here was in Fermat’s copy of
the Arithmetica, an ancient Greek text written by Dio-
phantus of Alexandria. The problems given in this text
provided the stimulus for many of Fermat’s discoveries
in number theory. The equation x
4
+ y
4
= z
4
arose from
problems concerning right-angled triangles
Fermat’s proof
Fermat gave sufficient details of his proof to enable it
to be reconstructed. However, the purpose of this note
is not to reproduce the original proof faithfully but to
modify and simplify it whilst retaining the historical con-
nection with right-angled triangles.
Theorem: A right-angled triangle with rational sides
cannot have two sides each with a length equal to a square
or twice a square.
Proof. Suppose such a triangle did exist. By scaling
by a square number we can further assume the sides to
have integer lengths. Then, any prime factor p of two of
the lengths would be a factor of all three lengths. Fur-
thermore, if p were odd, then p
2
would be a factor of two
of the lengths and thus of all the lengths. By cancelling
down as necessary, we can therefore assume the lengths
to be coprime in pairs. Then, by Euclid’s formula, there
are coprime positive integers a and b, one odd and one
even, such that the triangle is as shown.
FIG. 1:
Now y and z are both odd and so neither can be twice
a square. If they were both squares then the triangle
shown below would be a new solution.
FIG. 2:
Otherwise, just one of y and z is a square and x = 2ab
is a square or twice a square. Then each of a and b is a
square or twice a square and one of the triangles shown
below would be a new solution.
FIG. 3:
In all cases, the new solution has a smaller hypotenuse
than the original triangle. Since there cannot be an in-
finite series of decreasing hypotenuses, there can be no
triangle with the required properties.