Search for a tool
Chinese Remainder

Tool to compute congruences with the chinese remainder theorem. The Chinese Remainder Theorem helps to solve congruence equation systems in modular arithmetic.

Results

Chinese Remainder -

Tag(s) : Mathematics,Arithmetics

dCode and you

dCode is free and its tools are a valuable help in games, puzzles and problems to solve every day!
You have a problem, an idea for a project, a specific need and dCode can not (yet) help you? You need custom development? Contact-me!

Team dCode read all messages and answer them if you leave an email (not published). It is thanks to you that dCode has the best Chinese Remainder tool. Thank you.

Chinese Remainder

Chinese Remainder Calculator

Tool to compute congruences with the chinese remainder theorem. The Chinese Remainder Theorem helps to solve congruence equation systems in modular arithmetic.

What is the Chinese Remainder Theorem ?

The original problem is to consider a number of elements which we know the remainder of their Euclidean division.

If they are arranged by 3 there remains 2. If they are arranged by 5, there remain 3 and if they are arranged by 7, there remain 2. How many objects are there?

Consider a list of k coprimes integers $$n_1, ..., n_k$$ and their product $$n = \prod_{i=1}^k n_i$$. For all integers $$a_1, ... , a_k$$, it exists another integer $$x$$ which is unique modulo $$n$$, such as :

$$\begin{matrix} x \equiv a_1\pmod{n_1} \\ \ldots \\ x \equiv a_k\pmod{n_k} \end{matrix}$$

How to calculate chinese remainder?

Software accepts numbers written in couple (remainder, modulus), but is may be easier to write lines of x = A MOD B

(2,3),(3,5),(2,7) => x = 23

x = 2 mod 3
x = 3 mod 5
x = 2 mod 7
=> x = 23