Abstract
The most interesting and famous problem that puzzled the mathematicians all around the world is much likely to be the Fermat’s Last Theorem. However, since the Theorem was proposed, people can’t find a way to solve the problem until Andrew Wiles proved the Fermat’s Last Theorem through a very difficult method called Modular elliptic curves in 1995. In this paper, I firstly constructed a geometric method to prove Fermat’s Last Theorem, and in this way we can easily get the conclusion below: If a and b are integer and a = b, n ∈ Q and n > 1, the value of c satisfies the function an + bn = cn that can never be integer; if a, b and c are integer and a ≠ b, n is integer and n > 2, the function an + bn = cn cannot be established.
Highlights
The Fermat’s Last Theorem was proposed by French famous mathematician Pierre de Fermat in 1637, it was called the last theorem because it was the theorem of Fermat that can be proved at last, which means to prove the theorem is very difficult
In 1753, the famous Swiss mathematician Euler said in a letter to Goldbach that he proved the Fermat conjecture at n = 3, and his proof was published in the book Algebra Guide in 1770 [2]
We only discuss the condition of 0 < t < b, so the value of t satisfies the requirement is: t =−a + n an + bn we have found a solution for the equation of degree n with one unknown in function (18), and the solution of t is the function (19) and (20)
Summary
The Fermat’s Last Theorem was proposed by French famous mathematician Pierre de Fermat in 1637, it was called the last theorem because it was the theorem of Fermat that can be proved at last, which means to prove the theorem is very difficult. What’s more, many theorem were proposed in order to prove the Fermat’s Last Theorem, such as Modell conjecture, Taniyama-Shimura theorem. People tried to propose another theorem to indirectly prove the Fermat’s Last Theorem, but the relationship between two theorems is not very clear, the proof is hard to be verified.
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