Sequential Fractions

Number Theory Level 5

\[\large \left \{\dfrac{1}{2003}, \dfrac{2}{2002}, \dfrac{3}{2001}, \dfrac{4}{2000}, \ldots, \dfrac{2003}{1} \right \} \]

For each of the 2003 fractions above, the sum of the numerator and denominator equal 2004. Find the number of fractions less than 1 which are irreducible.