I just started a diploma in software development. Right now we're starting out with basic Java and such (so right from the bottom you might say) - which is fine, I have no programming experience apart from knowing how to do "Hello World" in Java.

I keep hearing that mathematics is pertinent to coding, but how is it so? What general examples would show how mathematics and programming go together, or are reliant on one another?

I apologize of my question is vague, I'm barely starting to get a rough idea of the kind of world I'm stepping into as a code monkey student...


Question: Let a and b be relatively prime integers and let k be any integer. Show that a + bk and b are also relatively prime.
Answer: HINT:

Let integer $d$ divides both $a+bk, b$

$\implies d$ divides $a+bk-k(b)=a$

$\implies d$ divides $a,b$