From the prime factor decomposition, we can find that the common multiple of two numbers (or multiple numbers) must have:?
The common multiple of (1) must include all the prime factors in these numbers, and according to the relationship between these prime factors, we divide these prime factors into three categories, one is the common prime factor, the other is the unique prime factor, and the other is the one that no one has (if the number that no one has is 0, then the common multiple is the least common multiple). ?
② The minimum common multiple must be satisfied at the same time: each group has only one common prime factor, and all the unique prime factors of these numbers must be taken out, and no other prime factors are allowed. The product obtained by multiplying all these prime factors is the least common multiple of these numbers.
Number theory is the two original branches of mathematics, namely, arithmetic and geometry, and there are still problems. Traditional geometry withered and all problems were solved. However, the traditional arithmetic has accumulated more and more problems, and it has become a dense forest that is difficult to cross.
It used to be considered as pure mathematics, specializing in the properties of integers. Positive integers can be divided into "prime number", "composite number" and "1" according to multiplication properties. Prime numbers have produced many unsolved problems that ordinary people can understand, such as Goldbach conjecture. Although many problems are elementary in form, they actually require a lot of difficult mathematical knowledge. The research in this field has promoted the development of mathematics in a certain sense and spawned many new ideas and methods.
C.F. Gauss once said, "Mathematics is the queen of science, and number theory is the queen of mathematics."
The span of number theory from the early stage to the middle stage 1000-2000 is almost blank. The middle period mainly refers to15-16th century to19th century, which was developed by Fermat, Mei Sen, Euler, Gauss, Legendre Riemann, Hilbert and others.
Taking the idea of finding the general formula of prime numbers as the main line, we began to change from elementary number theory to analytic number theory and algebraic number theory, resulting in more and more unsolvable conjectures. In the 20th century, many difficulties still depend on the general formula of prime numbers, such as prime formula's Riemann conjecture. If we find the general formula of prime numbers, some difficult problems can now be transferred from analytic number theory to elementary number theory.