When the integer n > 2, the indefinite equation x n+y n = z n about x, y, z has no positive integer solution.

2. Four-color problem

Only four colors can be used in any plane map, so that countries with the same border can be painted with different colors. Expressed in mathematical language, the plane is arbitrarily subdivided into non-overlapping areas, and each area can always be marked with one of the four numbers 1, 2, 3, 4, without making two adjacent areas get the same number.

3. Goldbach conjecture

1 On June 7th, 742, the German mathematician Goldbach put forward a bold conjecture in a letter to the famous mathematician Euler: any odd number not less than 3 can be the sum of three prime numbers (for example, 7=2+2+3, when1was still a prime number). On June 30th of the same year, Euler wrote back another version of Goldbach's conjecture: any even number can be the sum of two prime numbers.

Extended data

The essence of the four-color theorem is the inherent property of a two-dimensional plane, that is, two straight lines in the plane that cannot intersect and have no common points. Many people have proved that it is impossible to construct five or more connected regions on the two-dimensional plane, but it does not rise to the level of logical relationship and two-dimensional inherent attributes, which leads to many wrong counterexamples. But these are precisely the textual research and development promotion of the rigor of graph theory.

The computer proves that although we have made tens of billions of judgments, we have only succeeded in a huge number of advantages, which does not conform to the strict logic system of mathematics, and there are still countless math enthusiasts involved.