Basic knowledge points of number theory (updated constantly ~)

 

Important Theorem 1: Assume that both A and B are positive integers and A> B. A = BQ + R, 0 <r <B. Q and R are both positive integers, and the maximum public factor of A and B is equal to the maximum public factor of B and R, that is, (a, B) = (B, R ).

Important Theorem 2: calculate the maximum public factor of several large numbers using the moving phase division. Calculate the two largest public factors first, and then compare the two numbers with other numbers to obtain the result.

Important Theorem 3: Assume that both A and B are positive integers, and the minimum public multiples of A and B are m, that is, {a, B} = m. if m' is a public multiple of A and B, there is M | M '.

4: Assume that A and B are positive integers. The maximum public factor of A and B is d, and the minimum public factor of A and B is m, that is, (a, B) = D. {A, B} = m, and AB = DM. We can first calculate the maximum common number, which is simple and quick.

5: if A is an integer greater than 1, the minimum factor of a greater than 1 must be a prime number.