In this publication, we will consider one of the most popular theorems in mathematics – Fermat’s Last Theorem, which received its name in honor of the French mathematician Pierre de Fermat, who formulated it in a general form in 1637.
Statement of the theorem
For any natural number n> 2 the equation:
an + bn = cn
has no solutions in non-zero integers a, b и c.
History of finding evidence
Despite the simple formulation of Fermat’s Last Theorem at the level of simple school arithmetic, the search for its proof took more than 350 years. This was done by both eminent mathematicians and amateurs, which is why it is believed that the theorem is the leader in the number of incorrect proofs. As a result, the English and American mathematician Andrew John Wiles became the one who managed to prove it. This happened in 1994, and the results were published in 1995.
Back in the XNUMXth century, attempts to find evidence for n = 3 was undertaken by Abu Mahmud Hamid ibn al-Khizr al-Khojandi, a Tajik mathematician and astronomer. However, his works have not survived to this day.
Fermat himself proved the theorem only for n = 4, which raises some questions about whether he had a general proof.
Also proof of the theorem for various n suggested the following mathematicians:
- for n = 3People: Leonhard Euler (Swiss, German and mathematician and mechanic) in 1770;
- for n = 5People: Johann Peter Gustav Lejeune Dirichlet (German mathematician) and Adrien Marie Legendre (French mathematician) in 1825;
- for n = 7: Gabriel Lame (French mathematician, mechanic, physicist and engineer);
- for all simple n <100 (with the possible exception of the irregular primes 37, 59, 67): Ernst Eduard Kummer (German mathematician).