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# Fermat's theorem and its role in the development of mathematics

Fermat's theorem, its mystery and endless searchsolutions occupy a unique position in mathematics. Despite the fact that a simple and elegant solution was not found, this task served as an impetus for a whole series of discoveries in the field of set theory and primes. The search for an answer turned into an exciting process of competition between the leading mathematical schools of the world, and also revealed a huge number of self-taught students with original approaches to some or other mathematical problems.

Pierre Fermat himself was a striking example of thisself-taught. He left behind him a whole series of interesting hypotheses and proofs, not only in mathematics, but also, for example, in physics. However, he became known largely due to a small entry in the fields of the then popular "Arithmetics" of the ancient Greek explorer Diophantus. This record read that after much thought he found a simple and "truly miraculous" proof of his theorem. This theorem, which went down in history as "a large Fermat theorem," argued that the expression x ^ n + y ^ n = z ^ n can not be solved if the value of n is greater than two.

Pierre Fermat himself, despite having been left in the fieldsexplanation, he did not leave any general solution after himself, many who took up the proof of this theorem, found themselves powerless. Many have tried to build on the evidence of Fermat's own proof of this postulate for a particular case, when n is 4, but for other variants it turned out to be unsuitable.

Leonard Euler at great effort has managedprove Fermat's theorem for n = 3, after which he was forced to abandon the search, finding them hopeless. With time, when new methods for finding infinite sets were introduced into the scientific revolution, this theorem found its evidence for the range of numbers from 3 to 200, but it was still not possible to solve it in general form.

A new impetus for Fermat's theorem was obtained at the beginning of the 20thcentury, when a prize of one hundred thousand marks was announced to the one who will find its solution. The search for a solution for a while turned into a real competition in which not only venerable scientists but also ordinary citizens participated: Fermat's theorem, the formulation of which did not presuppose any ambiguous interpretation, gradually became no less famous than the Pythagorean theorem, from which, by the way , she once came out.

With the appearance of the first arithmometers, and then powerfulcomputers it was possible to find the proofs of this theorem for an infinitely large value of n, but in general form the proof still failed. However, no one could refute this theorem either. Over time, interest in finding the answer to this riddle began to subside. In many respects this was due to the fact that further evidence was already coming at a theoretical level that the ordinary citizen can not do.

A peculiar end of the most interesting scientifican attraction called "Fermat's theorem" became the research of E. Wiles, which to date have been accepted as the final proof of this hypothesis. If there were doubts about the correctness of the proof itself, then with the correctness of the theorem itself all agree.

Despite the fact that no "elegant"the proof of Fermat's theorem never received, her search made a significant contribution to many areas of mathematics, greatly expanding the cognitive horizons of mankind.

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