[This account is adapted from What is Mathematics. ] Pierre de Fermat (1601-1665) had studied the work of Diaphantus, the ancient contributor to number theory, and was accustomed to making comments in the margin of his copy. Although he stated many theorems without bothering to give proofs, all of them have subsequently been proved, with but one significant exception:
While commenting on Pythagorean Numbers, Fermat stated that the equation (*) is not solvable in [positive] integers for any n greater than 2, but that the elegant proof which he had found was unfortunately too long for the margin in which he was writing.
The theorem was finally proved in the mid 1990s by Andrew Wiles of Princeton University.
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