Linear Diophantine equation - Find all integer solutions Using the linear Diphantine equation 
  121x + 561y = 13200

(a)    Find all integer solutions to the equation.
(b)    Find all positive integer solutions to the equation.
edit: The answer I have for (a) is an equation: 
$x=16800 + 51n$
$y=-3600-11n$
where $n \in \mathbb Z. $
 A: HINT: 
First check if the greatest common divisor of 121 and 561 is a multiple of 13200. If so then this equation has a solution, otherwise it doesn't. Also it would be wise to divide by the greatest common divisor, so you'll work with smaller numbers.
And to obtain solutions apply the Euclidean Division Algorith. So you have:
$$561 = 4 \cdot 121 + 77$$
$$121 = 1 \cdot 77 + \cdots$$
Can you spot the pattern? Then going backwards you should be able to obtain one solution and quite easily a closed form of the solution. Then you can check when both solutions are positive.
Also I'm pretty sure there are a lot of nice books and video tutorials about solving a linear Diophantene equation on the internet. This one is quite simple and easy to follow.
A: Dividing the equation by the gcd 11, you get 11x + 51y = 1200. The complete solution to this equation is x = 21 + 51n and y = 19 - 11n. This is equivalent to the solution above x = 16800 + 51n and -3600 - 11n. The only positive integer solutions are (21,19) and (72,8).
