# System of congruence

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)

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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