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    System of congruence

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    I need to know how to find the system of congruence for the following:

    x = 5 (mod 6)
    x = 3 (mod 10)
    x = 8 (mod 15)

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    https://brainmass.com/math/discrete-math/system-congruence-233767

    Solution Preview

    First, we can rewrite the system as follows.
    (1) x = 5 (mod 6) is equivalent to: x = 5 (mod 2) and x = 5 (mod 3)
    Then x = 1 (mod 2) and x = 2 (mod 3)
    (2) x = 3 (mod 10) is equivalent to x = 3 (mod 2) and x = 3 (mod 5)
    Then x = 1 (mod 2) and x = 3 (mod 5)
    (3) x = 8 (mod 15) is equivalent to x = 8 (mod 3) ...

    Solution Summary

    This provides an example of finding a system of congruence.

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