Chinese remainder theorem proof
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8 Terms
Chinese Remainder Theorem formula
Uniqueness 1
Suppose that x and y are both solutions to all the congruences.
As x and y give the same remainder when divided by ni,
their difference x − y is a multiple of each ni.
Uniqueness 2
As the ni are pairwise coprime, their product N also divides x − y,
and thus x and y are congruent modulo N
Uniqueness 3
If x and y are supposed to be non-negative and less than N (as in the first statement of the theorem), then their difference may be a multiple of N only if x = y.
(0 is a multiple of every integer)
Existence using Lagrange Interpolation 1
Existence using Lagrange Interpolation 2
Existence using Lagrange Interpolation 3
Existence using Lagrange Interpolation 4
Note 
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