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The 17th-century mathematician Pierre de Fermat wrote about this in 1637 in his copy of Claude-Gaspar Bachet's translation of the famous Arithmetica of Diophantus: "I have discovered a truly remarkable proof but this margin is too small to contain it". (Original Latin: "Cuius rei demonstrationem mirabilem sane detexi hanc marginis exiguitas non caperet.") However, no correct proof was found for 357 years.
This statement is significant because all the other theorems proposed by Fermat were settled, either by proofs he supplied, or by rigorous proofs found afterwards. Mathematicians were long baffled, for they were unable either to prove or to disprove it. The theorem was therefore not the last that Fermat conjectured, but the last to be proved. The theorem is generally thought to be the mathematical result that has provoked the largest number of incorrect proofs.
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 infinity of them (even excluding trivial solutions for which a, b and c have a common divisorNumber theory In mathematics, a divisor of an integer n also called a factor of n is an integer which evenly divides n without leaving a remainder. For example, 7 is a divisor of 42 because 42/7 6. We also say 42 is divisible by 7 or 42 is a multiple of 7). According to Fermat's last theorem, no such solution exists when the exponent 2 is replaced by a larger integer number.
While the theorem itself has no known direct use (e.g., 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 only an unimportant mathematical curiosity. Moreover, the search for a proof has initiated research about many important mathematical topics.
The theorem needs only to be proven for n=4 and in the case where n is an oddOdd has several meanings. Within mathematics: an integer is odd if it cannot be divided by two; see even and odd numbers a function f defined on the real numbers is odd if f ''x &minus f &minus x for all x see even and odd functions a permutation of a fin prime numberIn mathematics, a prime number or prime for short, is a natural number whose only distinct positive divisors are 1 and itself; otherwise it is called a composite number . Hence a prime number has exactly two divisors. The number 1 is neither prime nor com. For various special exponents n, the theorem had been proved over the years, but the general case remained elusive.
Fermat himself proved the case n=4, while Euler proved the theorem for n=3. The case n=5 was proved by Dirichlet and Legendre in 1825Events January 4 King Ferdinand I of the Two Sicilies dies and is succeeded by his son Francis I of the Two Sicilies. February 9 After no presidential candidate received a majority of electoral votes, the United States House of Representatives elects John, and the case n=7 by Gabriel LaméGabriel Lam ( July 22, 1795, Tours, France May 1, 1870, Paris, France) was a French mathematician. He was well known for his notation and study of classes of ellipse-like curves, now known as Lame curves: : where n is any positive real number. He is also in 1839.
In 1983 Gerd Faltings proved the Mordell conjecture, which implies that for any n > 2, there are at most finitely many coprime integers a, b and c with an + bn = cn.
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