Question: I have scoured my textbook for the concept alluded to in the title of this thread; however, my textbook has failed, in that it provides no such information.

Does anyone know of some resources for this concept?

EDIT:

For instance, let me post a problem I am working on:

An instructor has given a short test consisting of two parts. For a randomly selected student, let $X=$ the number of points earned on the first part and $Y=$ the number of points earned on the second part. Suppose that the joint pmf of X and Y is given in the accompanying table.

p(x,y) 0 | 5 | 10 | 15

0 | 0.02| 0.06| 0.02| 0.10

5 | 0.04| 0.15| 0.20| 0.10

10| 0.01| 0.15| 0.14| 0.01

a) If the score recorded in the grade book is the total number of points earned on two parts, what is the distribution of $X+Y$ and what is the expected recorded score $E(X+Y)$

b) If the maximum of the two scored is recorded, what is the distribution of the maximum score $Max(X,Y)$ ad the expected maximum score $E(Max(X,Y))$

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Now that I re-look at this question, I doubt whether I can solve any of it. At any rate, how do I find the distribution of $X+Y$?

Answer: 
Every $ma+nb$ is a multiple of $\gcd(a,b)$, so also the smallest positive such number is a multiple.
From [Bezout's identity](http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity) we have that $\gcd(a,b)=sa+rb$ for some $r,s\in\mathbb Z$.  

Also $\gcd(a,b)\mid a , \ \gcd(a,b)\mid b$ and therefore for any $n,m\in\mathbb Z$ with $ma+nb>0\Rightarrow ma+nb=k\cdot\gcd(a,b)$ for some $k\in\mathbb N$.  

Since $sa+rb=1\cdot\gcd(a,b)$ it follows that $\gcd(a,b)$ is the smallest element of $\lbrace ma + nb : m, n\in\mathbb{Z}\text{ and }ma+nb>0\rbrace$.