<s>[INST] modulo question I thought you could only mod positive numbers but then I saw this 
and became confused...How does this even work ? how can you have negatives?
$$\begin{align*}
-8 &\equiv 7 \pmod{5}\\
2 &\equiv -3 \pmod{5}\\
-3 &\equiv -8\pmod{5}
\end{align*}$$
Actually....What I thought was that mod just means how many times a number goes into another number while leaving a remainder...
But after some reading I find that negative values can be equal to positive values as long as some value-remainder is divisible by the modulus. But it doesnt make sense to me that the remainderi n these equation is greater than the modulus AND that the remainder is positive while answer on left end is negative. 
 [/INST] In simple terms mod gives you remainder.  Also if $a\equiv b\pmod{n}$, then $b\equiv a\pmod{n}$, because $n$ divides $(a-b)$, then $n$ also divides $(b-a)$.  With the examples you had, for instance 
$$
\begin{align*}
-8 &\equiv 7 \pmod{5}\\
2 &\equiv -3 \pmod{5}\\
-3 &\equiv -8\pmod{5}
\end{align*}
$$
$-8 \equiv 7 \pmod{5} \hspace{5pt} \Rightarrow \hspace{5pt} 7 \equiv -8 \pmod{5}$ or in other words $5$ divides $7-(-8) = 15$, i.e. $5 | 15$.
Just like with positive values you could add $5$, on the negative side you could also subtract $5$.  For instance if $x \equiv 1 \pmod{5}$, then $x \equiv -4 \pmod{5}$ and also $x \equiv 6 \pmod{5}$.
In simple words that is all about mod.  But if you study Number Theory, there are lot of interesting things you would learn.
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