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    Chinese Remainder Theorem

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    Need to prove two parts and must follow the Chinese Remainder Theorem.

    Let be polynomials with integer coefficients of the same degree d. Let be integers which are relatively prime in pairs (i.e., ( for i j). Use the Chinese Remainder Theorem to prove there exists a polynomial f(x) with integer coefficients and of degree d with
    mod , mod ,..... mod
    i.e., the coefficient of f(x) agree with the coefficients of mod .
    Show that if all the are monic, then f(x) may also be chosen monic.
    [Apply the Chinese Remainder Theorem in Z to each of the coefficients separately.]

    Please see the attached file for the fully formatted problems.

    © BrainMass Inc. brainmass.com October 9, 2019, 7:17 pm ad1c9bdddf
    https://brainmass.com/math/algebra/chinese-remainder-theorem-113607

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    Suppose , , ...

    Solution Summary

    The Chinese Remainder Theorem is applied to monic functions.

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