If and are natural numbers so that prove that is divisible with .
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If $p$ and $q$ are natural numbers so that $$\frac{p}{q}=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+ \ldots -\frac{1}{1318}+\frac{1}{1319},$$ prove that $p$ is divisible with $1979$.
Source: Međunarodna matematička olimpijada, shortlist 1979
Školjka 
and 
are natural numbers so that 
prove that 
.