gcd(2a + 1, 9a + 4) =

Step 1 (Apply Euclidean Algorithm): We want to find the greatest common divisor of $2a+1$ and $9a+4$ for any integer $a$. We apply the GCD property $\gcd (x,y)=\gcd (x,y-kx)$:

Step 2 (Second Reduction Step): Now we apply the same property again:

Step 3 (Conclusion): Since the GCD reduces to $\gcd (a,1)$, it is equal to 1 for all integer values of $a$.