Artificial intelligent assistant

proving that given fraction is irreducible. Prove that for every natural number n, fraction $\frac{21n+4}{14n+3}$ is irreducible. I deduced that if we can prove that numerator and denominator have 1 as their GCD, we can get the result, but I cannot get it from thereon.

Going by Euclidean algorithm: $$ GCD(21n+4, 14n+3) = GCD(7n+1, 14n+3) = GCD(7n+1, 1) = 1$$

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