文档介绍：Is There a “Simple” Proof of Fermat’s Last Theorem?
Is There a “Simple” Proof of
Fermat's Last Theorem?
A New Approach
by
Peter Schorer
(Hewlett-Packard Laboratories, Palo Alto, CA (ret.))
2538 Milvia St.
Berkeley, CA 94704-2611
Email: peteschorer@
Phone: (510) 548-3827
Jan. 10, 2005
Key words: Fermat's Last Theorem
1
Is There a “Simple” Proof of Fermat’s Last Theorem?
Introduction
Fermat's Last Theorem (FLT) states that:
For all n > 2, there do not exist x, y, z such that xn + yn = zn,
where x, y, z, n, are positive integers.
Until the mid-1990s, this was the most famous unsolved problem in mathematics. It was
originally stated by the 17th century mathematician Pierre de Fermat (1601-65).
“In about 1637, he annotated his copy (now lost) of Bachet’s translation of Diophantus’
Arithmetika with the following statement:
Cubem autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et gener-
aliter nullam in infinitum ultra quadratum potestatem in duos ejusdem nominis fas est
dividere: cujus rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non
caparet.
“In English, and using modern terminology, the paragraph above reads as:
There are no positive integers such that xn + yn = zn for n > 2 . I’ve found a remarkable
proof of this fact, but there is not enough space in the margin [of the book] to write it.”
— Dept. of Mathematics, University of North Carolina at Charlotte
()
For more than 350 years, no one was able to find a proof using the mathematical tools at Fer-
mat’s disposal, or using any other, far more advanced, tools either, although the attempts produced
numerous results, and at least one new branch of algebra, namely, ideal theory. Then in summer
of 1993, a proof was announced by Princeton University mathematics professor Andrew Wiles.
(Actually, Wiles announced a proof of a special case of the Shimura-Taniyama Conjecture — a
special