How is the Euclidean Algorithm used to solve IMO 1959 Problem 1? Problem 1 : Prove that the fraction $\frac{21n+4}{14n+3}$ is irreducible for every natural number $n$.
I understand that it can be solved using the Euclidean Algorithm, but how would the solution look like? I know the Euclidean Algorithm, but don't understand how it is applied here. 

HINT:
If integer $d$ divides $21n+4,14n+3$
$d$ must divide $3(14n+3)-2(21n+4)=1$
The basic idea was to eliminate $n$ and find a constant that must be divisible by $d$
