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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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Solution Summary

This provides an example of finding a system of congruence.

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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) ...

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