1637, when reading the Latin translation of Diophantine's arithmetic, P.de Fermat wrote next to Proposition 8 that this proposition has a general solution formula of Pythagorean integer equation: "Divide the cubic number of an integer by the sum of two cubic numbers, or divide the fourth power of an integer by the sum of two quartic powers, or generally divide a power higher than quadratic by the sum of two powers of the same power." In this regard, I am sure that I have found a' unique and wonderful reliable proof method'. Unfortunately, the space here is too small to write down. " .
Four-color conjecture: "Any map with only four colors can make countries with the same border have different colors." Expressed in mathematical language, it means "divide the plane into non-overlapping areas at will, and each area can always be marked with one of the four numbers 1234, without making two adjacent areas get the same number." The contiguous zone mentioned here means that there is a whole section of boundary that is common. Two regions are not adjacent if they intersect at one point or a limited number of points. Because painting them the same color won't cause confusion. The content of the four-color problem is "any map with only four colors can make countries with the same border have different colors." In other words, a map only needs four colors to mark it, which will not cause confusion.
Goldbach conjecture: Goldbach put forward the following conjecture in the letter 1742 to Euler: any even number greater than 2 can be written as the sum of two prime numbers. But Goldbach himself could not prove it, so he wrote to the famous mathematician Euler to help prove it, but until his death, Euler could not prove it. Because the convention that "1 is also a prime number" is no longer used in mathematics, the modern statement of the original conjecture is that any integer greater than 5 can be written as the sum of three prime numbers. Euler also put forward another equivalent version in his defense, that is, any even number greater than 2 can be written as the sum of two prime numbers. Today's popular conjecture is said to be Euler's version. Any sufficiently large even number can be expressed as the sum of a number with no more than one prime factor and another number with no more than b prime factors, and the proposition is called "a+b". 1966, Chen Jingrun proved that "1+2" was established, that is, "any large enough even number can be expressed as the sum of two prime numbers, or the sum of a prime number and a semi-prime number".
The proof of Fermat's conjecture was completed by British mathematician andrew wiles in 1994, hence the name Fermat's last theorem. The proof of the four-color conjecture was completed by American mathematicians Appel and Haken in 1976 with the help of computers, so it is called the four-color theorem. Goldbach's conjecture has never been solved, and the best result was obtained by China mathematician Chen Jingrun in 1966. The similarity of these three problems lies in their simple topics and profound connotations, which have influenced mathematicians from generation to generation.