I am having some trouble learning how to manipulate congruences, and have two questions on things I don't understand:

1. I understand that the following:

$\displaystyle a +_n (b +_n c) \equiv a + (b +_n c) \pmod{n}$

comes directly from the definition of the rule for $\displaystyle +_n$

But why is the following also true?:

$\displaystyle a + (b +_n c) \equiv a + (b + c) \pmod{n}$

2. Why is the following true?

$\displaystyle 3^{18*3+1} \equiv (3^{18})^3 * 3 \pmod{19}$

Thanks,