章 539: Chapter 319: Professor Zhao's First Lecture

Many famous mathematical conjectures in the world began with special case proofs, which is to say, proofs that focus on specific numerical values or regions. Fermat's Last Theorem started in the same way.

The content of Fermat's Last Theorem is simple--

When the integer n is greater than 2, the equation x^n + y^n = z^n has no positive integer solutions.

The equation also contains four unknowns, x, y, and z are fixed unknowns, and special case proofs usually target the exponent n.

Switzerland's famous mathematician Euler was the first to provide a proof for Fermat's Last Theorem in a letter to Goldbach. He stated that he had proven Fermat's Last Theorem for n=3, and his proof was published thirteen years later in the book "Algebraic Guidelines". The method he used was an "infinite descent" combined with a unique factor decomposition theorem for number systems, which was quoted many times by later mathematicians.