1. number theory: including arithmetic progression, geometric progression, Fibonacci series, etc. The numbers in these series increase or decrease according to certain rules.
2. Prime number rule: a prime number refers to a positive integer that can only be divisible by 1 and itself. In Olympic numbers, the distribution law and nature of prime numbers are often involved.
3. Factorization law: Factorization of a number refers to expressing the number as the product of several prime numbers. In Olympic mathematics, factorization is often needed to solve problems.
4. Law of greatest common divisor and least common multiple: The greatest common divisor of two or more numbers refers to the largest positive integer that can be divisible by these numbers at the same time, and the least common multiple refers to the smallest positive integer that can be divisible by these numbers at the same time. In Olympic numbers, it is often necessary to solve the greatest common divisor and the least common multiple.
5. Law of Fraction: Fraction refers to the ratio of numerator to denominator. In the Olympiad, it often involves the addition, subtraction, multiplication and division of fractions, comparison size and other issues.
6. Geometric laws: Geometric laws include properties, areas, perimeters, etc. In olympiad, it is often necessary to solve problems through geometric laws.
7. Law of Probability: Probability refers to the possibility of an event. In the Olympic Games, it is often necessary to calculate the probability of events or solve problems according to the probability.
8. Combination method: Combination refers to the combination method of selecting several elements from a given element. In the Olympiad, it is often necessary to calculate the number of combinations or solve problems according to combinations.