IMO Shortlist 1969 problem 34
Dodao/la:
arhiva2. travnja 2012. ![(HUN 1)](/media/m/3/c/b/3cbdd08fc9fb4f891724c0959ed54807.png)
Let
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
and
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
be arbitrary integers. Prove that if
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
is an integer not divisible by
![3](/media/m/b/8/2/b82f544df38f2ea97fa029fc3f9644e0.png)
, then
![(a + b)^{2k}+ a^{2k} +b^{2k}](/media/m/a/3/1/a314df7c20f21838c2e360525b972867.png)
is divisible by
%V0
$(HUN 1)$ Let $a$ and $b$ be arbitrary integers. Prove that if $k$ is an integer not divisible by $3$, then $(a + b)^{2k}+ a^{2k} +b^{2k}$ is divisible by $a^2 +ab+ b^2$
Izvor: Međunarodna matematička olimpijada, shortlist 1969