Question

[SOLVED] For those bored, here's a cute little number theory related problem.

Prove that the fraction \[{21n+4 \over 14n+3}\]is irreducible for all positive integers \(n\).

PS: It's a two line proof.

Answer 1

potato?

Answer 2

A hint is below in white LaTeX font. \[\color{white}{\text{prove that the numerator and the denominator are coprime}} \]

Answer 3

\[3 (14 n+3)-2 (21 n+4)=1
\]
Applu Bezout and see if you can finish it.