Finding GCD of $95$ and $39$ My Algebra instructor gave us this problem which is to find gcd of $95$ and $39$ and express it as $95x+39y$.  Also are $x$, $y$ unique?
Now they are relatively prime so GCD is $1$.  I have no clue how to find $x$ and $y$ and if they are unique or not.
Thanks!

Although you could use the extended Euclidean algorithm to calculate that value, sometimes it's simpler to use Euler's theorem and exponentiation by squaring.
I don't want to solve your problem for you, so I will use similar numbers $94$ and $51$ instead.
More precisely, say we want to find $x$ and $y$ such that $94x+51y = \gcd(94,51) = 1$. This implies that $94x=1 \pmod{51}$, thus 
\begin{align}
x & = 94^{\phi(51)-1}    &\pmod{51} \\
  & = 94^{(17-1)(3-1)-1} &\pmod{51} \\
  & = 94^{31}            &\pmod{51} \\
  & = 94^{30+1}    &\pmod{51} \\
  & = 94\cdot(94^{15})^2 &\pmod{51} \\
  & = 94\cdot(94\cdot(94\cdot(94\cdot (94\cdot1^2)^2)^2)^2)^2 &\pmod{51} \\
  & = 94\cdot(94\cdot(94\cdot(94\cdot (94\cdot1^2)^2)^2)^2)^2 &\pmod{51} \\
  & = 19 &\pmod{51}
\end{align}
That means we can pick any $x = 19 \pmod{51}$ to get a solution. For example when $x = 19$ then $94\cdot 19 + 51y = 1$ gets us $y = \frac{1-94\cdot 19}{51} = -35$. On the other hand if $x = 19+51 = 70$ then $y=-129$.
I hope this helps $\ddot\smile$
