chinese remainder theorem in a sentence

However it is possible that cyclic subspaces do allow a decomposition as direct sum of smaller cyclic subspaces ( essentially by the Chinese remainder theorem ).
If we know the congruence classes modulo these two numbers, we know what the result is modulo 10 ( by the Chinese remainder theorem ).
This turns out to be equivalent to a system of simultaneous polynomial congruences, and may be solved by means of the Chinese remainder theorem for polynomials.
The factorial number system uses a varying radix, giving factorials as place values; they are related to Chinese remainder theorem and residue number system enumerations.
I did also use Mathematica, but that was only used to compute the last few steps involving the Chinese Remainder Theorem and some further trivial processing.

Each of the shares is represented in a congruence, and the solution of the system of congruences using the Chinese remainder theorem is the secret to be recovered.
For computing a resultant of polynomials with integer coefficients, it is generally faster to compute it modulo several primes and to retrieve the desired resultant with Chinese remainder theorem.
Given t \ pmod { l _ i } for all l _ i \ in S, the Chinese remainder theorem allows us to compute t \ pmod N.
:However, it is modding the exponents by 4 that would do the trick, because of a number theory thing called Totient function and the Chinese remainder theorem.
Anyway, yes, the story is obviously supposed to be an illustration of the Chinese remainder theorem . talk ) 10 : 35, 22 May 2009 ( UTC)

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