Tag:Common factor

  • Chapter 1: pythagorean array (2)

    Time:2020-12-10

    Pythagorean array theorem Pythagorean array theorem: each primitive Pythagorean array (a, B, c) (where a is odd and B is even) can be obtained from the following formula: a = st\\ b = \frac{s^2-t^2}{2}\\ c = \frac{s^2 + t^2}{2} amongs>t\geq 1Is any odd number that has no common factor.The proof process is as follows:Considering the […]

  • Chapter 5: divisibility and the greatest common factor (1)

    Time:2020-12-7

    Suppose m and N are integers,m\neq 0。 If n is a multiple of M, there exists an integer k such thatn= mk。 If M is divisible by N, we write it asm|n; ifmDo not dividen, we remember asm\nmid n。 For example, because6=3·2, so3|6。6The factor of is1,2,3。 Because there is no5A multiple of is equal to7, […]

  • Chapter 5: divisibility and the greatest common factor (2)

    Time:2020-12-6

    Euclidean algorithm The most effective way to find the greatest common factor of two numbers is Euclidean algorithm, which consists of a series of division with remainder until the remainder is zero. Before describing the general method, we use an example to illustrate:We calculategcd(36,132)The first step is132divide36Get quotient3And remainder24。 We write it down as 132 […]