Confused about modular notations I am little confused about the notations used in two articles at wikipedia. 

According to the page on Fermat Primality test

$
a^{p-1}\equiv 1 \pmod{m}$ means that when $a^{p-1}$ is divided by $m$, the remainder is 1. 

And according to the page on Modular Exponential

$c \equiv b^e \pmod{m}$ means that when $b^e$ is divided by $m$, the remainder is $c$. 

Am I interpreting them wrong? or both of them are right? Can someone please clarify them to me? 

Update: So given an equation say $x \equiv y \pmod{m}$, how do we interpret it? $y$ divided by $m$ gives $x$ as remainder or $x$ divided by $m$ gives $y$ as remainder?
They are both correct. The congruence sign is symmetric so c ≡ b^e is the same as b^e ≡ c.

However what it really means is this: a≡b (mod m) if and only if m|a-b (i.e. m divides a-b).
Mod, or modulas, is a binary operator, like '+'.  You write a mod b.  Writing a (mod b) is a bit like writing a (+ b).  That said, you might see a note in with your equations.  Just I might write time = money (minus taxes as previously discussed), that wordy chunk is part of my verbiage instead of my equation.

a mod b means that the remainder of dividing a by b.  For example, 27 mod 5 = 1 or (27 mod 5) + 2 = 3.

Neither of the equations listed makes any sense, because mod is binary.   You probably meant:

(a^(p-1)) mod m = 1

and

*c = (b^e) mod m