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p is divisible by 2003

Source: Pan African 2000

October 3, 2005

Problem Statement

Let pp and qq be coprime positive integers such that: pq=1−12+13−14⋯−11334+11335 \dfrac{p}{q}=1-\frac12+\frac13-\frac14 \cdots -\dfrac{1}{1334}+\dfrac{1}{1335} Prove pp is divisible by 2003.
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