Concerning some properties of Modular Arithmetic. Recently I came across a Wikipedia page concerning Modular Arithmetic. Some properties were stated there, but without any proof. I tried solving them. Most were solved but I got stuck up in two of them.
They are:-
1.If a ≡ b (mod n), then p(a) ≡ p(b) (mod n), for any polynomial p(x) with integer coefficients.
2.If c ≡ d (mod φ(n)), where φ is Euler's totient function, then a^c ≡ a^d (mod n)—provided that a is coprime with n.
I tried to prove them quite a few times, but failed.
Can someone please help me with these. The Wikipedia page is this. 
Thanks in advance!

By order, $$\begin{align*}a&\equiv_n b \\
\Rightarrow a^j&\equiv_n b^j\end{align*}\\
\Leftrightarrow ka^j\equiv_n kb^j,$$ and this for any $k,j\in\mathbb{Z}$ so you can basically make any poynomial that you want. For the second one I think that you are talking of $$c\equiv_{\varphi(n)}d\Rightarrow a^c\equiv_n a^d$$ if $(a,n)=1,$ this isn´t that hard to see, it´s only realizing what´s totient function structure.
