Chinese remainder theorem && expand Chinese remainder theorem

Chinese remainder theorem:

    Indeterminate Equation for solving a set of an algorithm called the Chinese remainder theorem. Also known as Remainder Theorem.

 

    Wherein m1, m2, m3 ... mk by pairwise relatively prime integers, find x smallest non-negative integer solution

 

 

 

 

 

PS:

Remainder nature:

  <1> of the remainder and the decisions and the remainder: 16 + 7 = 23 (16% 5 = 17% 5 = 2 23% 5 = 3 = "  1 + 2 = 3); 9 + 8 = 17 (9% 5 = 48% 17% 5 = 5 = 3 = 2 "(3 + 4) 2 = 5%)

  <2> the difference of the remainder remainder determined difference: 6 - 2 = 4 (6% 5% 5 = 2 = 1 = 2 "(1-2) 4 = 5%) 

  <3> Integrated remainder of the product determines the remainder: 12 * 3 = 36 (12% 5% 5 = 3 = 2 = 3 "(2 * 3) 5 = 1%) 

  <4> remainder determines a power of a power of I: 3 ^ 1 2 = 2017% (3% 2 = 1 1 = 1 2 ^ 2017%)

Chinese remainder theorem:

   <1> I added with: the same remainder, common multiple of the divisor Pn = I plus x% 3 = 2 x% 4 = 2 x = 3 * 4 * n + 2 (n> = 1)

   <2> and with additive: a common multiple of the divisor and the remainder and divisor Pn = the same as the sum of x% 5 = 1 x% 4 = 2 x = 20 (the least common multiple) * n + 6

   <3> Save difference with a difference: the same as the difference between the divisor and the number of I, the common multiple shear difference divisor Pn = x% 4 = 3 x% 5 = 4 x = 60 (least common multiple) * n-1