Fermat's last theorem

Fermat's last theorem (sometimes abbreviated as FLT and also called Fermat's great theorem) is one of the most famous theorems in the history of mathematics. It states that:

Mathematical context

Fermat's last theorem is a generalization of the Diophantine equation a2 + b2 = c2, which is linked to the Pythagorean theorem. Ancient Greeks and Babylonians knew that this equation has integer solutions, such as (3,4,5) (32 + 42 = 52) or (5,12,13). These solutions are known as Pythagorean triples, and there exist an infinite number of them (even excluding trivial solutions for which a, b and c have a common divisor). According to Fermat's last theorem, no such solution exists when the exponent 2 is replaced by a larger integer number.

Related Topics:
Diophantine equation - Pythagorean theorem - Pythagorean triple - Infinite - Divisor

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While the theorem itself has no known direct use (i.e. it has not been used to prove any other theorem), it has been shown to be connected to many other topics in mathematics, and is not merely an unimportant mathematical curiosity. Moreover, the search for a proof has initiated research about many important mathematical topics.

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