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? 

x ≡ y (mod m)

is equivalent to:
x divided by m gives the same remainder as y divided by m

So, in your first example:
a^(p-1) ≡ 1 (mod m)

is equivalent to:
a^(p-1) divided by m gives the same remainder as 1 divided by m
But 1 divided by m gives remainder 1, so the above becomes:
a^(p-1) divided by m gives remainder 1

In your second example:
c ≡ b^e (mod m)

is equivalent to:
c divided by m gives the same remainder as b^e divided by m
But (assuming that 0 <=c < m) we have c divided by m gives remainder c, so the above becomes:
c is the remainder that b^e divided by m gives.

As it seems that the notation may be confusing, let me note that 
x ≡ y (mod m)

should be read as:
[ x ≡ y ] (mod m)         --- the (mod m) is applied to the whole congruence

and not as:
x ≡ [ y (mod m) ]         --- and not just to the right part.

