The Proof of Fermat's Last Theorem

The Proof of Fermat's Last Theorem

Overview

But one cannot split a cube into two cubes, nor a fourth power into two fourth powers, nor in general any power in infinitum beyond the square into two like powers. I have uncovered a marvelous demonstration indeed of this, but the narrowness of the margin will not contain it.

These words, written by Pierre de Fermat (1601-1665) in the margin of his copy of Diophantus's Arithemetica, have challenged and sometimes haunted mathematicians for more than 350 years. When a successful proof of Fermat's Last Theorem was finally found in 1993, it ended centuries of interesting and often controversial attempts to solve this famous problem.

Background

In modern algebraic terms, the theorem states that the equationxⁿ + yⁿ = zⁿhas no whole number solutions for n > 2. If n = 2, we have the famous Pythagorean Theorem:x² + y² = z²For instance, if x = 3, y = 4, and z = 5, we have,3² + 4² = 5²9 + 6 = 25This is only one of an infinite number of solutions, called Pythagorean triples. But Fermat claimed that if n were three or four or any other whole number larger than 2, then there were no solutions to the equation.

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