You remember the times with school Pythagorean theorem: the square of the hypotenuse equals the sum of a rectangular triangle squares legs. Perhaps you remember the classic rectangle and triangle with the parties, the length of which relate both 3: 4: 5. It looks like the Pythagorean theorem:
32 + 42 = 52
This is an example of the generalized solution Pythagorean equation in nonzero whole numbers when n = 2. Great Fermat Theorem (it is also known as "Big" and Fermat's theorem "was last Fermat theorem") is the assertion that while values n> 2 type equation xn + yn = zn has no nonzero solutions in the natural numbers.
Great History of Fermat's theorem is very interesting and instructive, and not just for math. Pierre de Fermat contributed to the development of a variety of areas of mathematics, but most of its scientific heritage has been published only posthumously. The fact is that the mathematics for Farm was something like a hobby, not a professional occupation. He corresponded with the leading mathematicians of his time, but did not publish their work sought. Farm Works found mainly in the form of private correspondence and records obryvochnyh, often made in the fields of various books. It is in the margin (second volume of ancient Greek "Arithmetic" Diofanta. - Prime. Translator) shortly after the death of mathematics descendants and found the wording of the famous theorem and the registry:
"I found this a truly wonderful proof, but those fields are too narrow for him."
Alas, apparently Fermat never write udosuzhilsya harvested them "proof" wonderful, and his descendants have sought unsuccessfully for more than three centuries. Of the scattered Scientific Heritage Farm, which contains many astonishing allegations, it has consistently failed Great Theorem solution.
Who are taken not only for the proof of Fermat's theorem Great - all in vain! Another great French mathematician René Descartes (René Descartes, 1596-1650), called "The Farm" unfortunately, and the English mathematician John Wallis (John Wallis, 1616-1703) - and is "chertovym Frenchman." Fermat himself, the truth, all the same evidence left behind his theorem for the case n = 4. In testimony for n = 3 coped great Swiss-XVIII century Russian mathematician Leonard Eyler (1707-83), then failing to find evidence for n> 4, jokingly offered to arrange residence searched Farm to find the key to the lost of evidence. In the XIX century, new methods of the theory of numbers allowed to demonstrate approval for many of whole numbers in the 200, but, again, not for everyone.
In 1908 Prize was established in the amount of 100000 DM for this task. The prize fund bequeathed by German industrialist Paulo Volfskelem (Paul Wolfskehl), which, according to tradition, was going to commit suicide, but it fell Great Fermat theorem that changed to die. With the advent of adding machines, computers and then became a slat n values rise above all - up to 617 by the beginning of the Second World War, to 4001 in 1954 to 125000 in 1976. In late XX century powerful computers military laboratories in Los Alamos (New Mexico, USA) were programmed to the task Farm in the background (similar to the regime of personal computer screen saver). Thus was able to show that the theorem is true for extremely large values of x, y, z and n, but strict proof of this could not serve as any values or troika n natural numbers could disprove the theorem as a whole.
Finally, in 1994, the English mathematician Andrew John Wiles (Andrew John Wiles, district. 1953), working in Princeton, has published the Great proof of Fermat's theorem, which, after some improvements had been recognized as exhaustive. Proof has taken more than a hundred pages of magazines and based on the use of modern apparatus of higher mathematics, which in the era of Fermat was not drafted. So what then was referring Farm, leaving books in the fields announcement that the evidence they found? Most mathematicians with whom I spoke on this subject, pointed out that for centuries accumulated more than enough evidence Great ill of Fermat's theorem, and that is likely to find himself Fermat such evidence, but has not been able to see in it a mistake. However, it is possible that all the same there are some short and elegant proof of Fermat's theorem the Great, which no one has so far not found. In certain that only one thing: Today we do know that the theorem is correct. Most mathematicians, I think, unconditionally agree with Andrew Uaylsom, who remarked about his evidence: "Now, finally, my mind calm."
