IMO Shortlist 1979 problem 7
Dodao/la:
arhiva2. travnja 2012. If
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
and
![q](/media/m/c/1/d/c1db9b1124cc69b01f9a33595637de69.png)
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},](/media/m/0/6/8/068b442f299904e1413966d477b918d2.png)
prove that
![p](/media/m/1/c/8/1c85c88d10b11745150467bf9935f7de.png)
is divisible with
![1979](/media/m/1/d/1/1d1bb3a0e59dc31d7be0584e487ed140.png)
.
%V0
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 $1979$.
Izvor: Međunarodna matematička olimpijada, shortlist 1979