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Common Solutions for Congruences

Find all common solutions to the congruences

(in the following notations the = is meant to be a congruence symbol)

x=2(mod 3), x=1(mod 4), x=3(mod 5), x=4(mod 7)

Solution Preview

We can use the Chinese remainder Theorem.
3, 4, 5, 7 are relatively prime to each other.
Let m=3*4*5*7=420
M1=420/3=140, ...

Solution Summary

This shows how to use Chinese Remainder Theorem to find solutions to congruences.