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. 

The euclidean algorithm works just as usual. We have
$$
\gcd(21n+4,14n+3)\\
=\gcd(21n+4-(14n+3),14n+3)\\
=\gcd(7n+1,14n+3)\\
=\gcd(7n+1,14n+3-2(7n+1))\\
=\gcd(7n+1,1)=1
$$
