1, Fermat's conjecture:
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
Advance the "a+b" problem
1920, Norway Brown proved "9+9".
1924, Latmach of Germany proved "7+7".
1932, Esterman proved "6+6".
1937, Lacey in Italy successively proved "5+7", "4+9", "3+ 15" and "2+366".
1938, Bukit Tiber of the Soviet Union proved "5+5".
1940, Bukit Tiber of the Soviet Union proved "4+4".
1956, Wang Yuan of China proved "3+4". Later, "3+3" and "2+3" were proved.
1948, Rini of Hungary proved "1+ c", where c is a large natural number.
1962, Pan Chengdong of China and Barba of the Soviet Union proved "1+5", and Wang Yuan of China proved "1+4".
1965, Buchwitz Taber and vinogradov Jr. of the Soviet Union and Pemberley of Italy proved "1+3".
1966, China Chen Jingrun proved "1+2".