Y by Adventure10, Mango247
Let
and
be coprime positive integers such that:
![\[ \dfrac{p}{q}=1-\frac12+\frac13-\frac14 \cdots -\dfrac{1}{1334}+\dfrac{1}{1335} \]](//latex.artofproblemsolving.com/b/d/3/bd374388fe6b84fbcd66e23a7956f2fbeebe4c28.png)
Prove
is divisible by 2003.


![\[ \dfrac{p}{q}=1-\frac12+\frac13-\frac14 \cdots -\dfrac{1}{1334}+\dfrac{1}{1335} \]](http://latex.artofproblemsolving.com/b/d/3/bd374388fe6b84fbcd66e23a7956f2fbeebe4c28.png)
Prove

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