Problem - 2506
How many positive integers, not exceeding $2019$, are relatively prime to $2019$?
First, $2019 = 3 \times 673$. Then, applying Euler's $\varphi$ function gives: $$\varphi(2019)=2019\times \left(1-\frac{1}{3}\right)\left(1-\frac{1}{673}\right)=\boxed{1344}$$