Solve the systems x ≡ 1 (mod 2), x ≡ 2 (mod 3). x ≡ 2 (mod 5), 2x ≡ 3 (mod 7), 3x ≡ 4 (mod 11). x ≡ 31 (mod 41), x ≡ 59 (mod 26).

Working with the relation of "congruence modulo" is a bit hard, so lets convert this congruence modulo relations to equations.

We know that '' means 2 divides ''. Keep in mind I can't add a three line "equality" symbol in ...

The previous can be written with this statement:

In which '' is any integer.

From the previous equation is very easy to see that ''.

We write the remaining congruence modulo relations as equations and solve for them in similar fashion: 







Now we solve for the x's, remember, k is any integer!