MEMO 2007 ekipno problem 8
Dodao/la:
arhiva28. travnja 2012. Find all positive integers
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
with the following property: There exists an integer
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
so that
![(a+k)^{3}-a^{3}](/media/m/c/5/f/c5f4e2ea7dc867adf2a6c3a8c1df8795.png)
is a multiple of
![2007](/media/m/3/f/4/3f405241bc274df2b17a4f30ef472364.png)
.
%V0
Find all positive integers $k$ with the following property: There exists an integer $a$ so that $(a+k)^{3}-a^{3}$ is a multiple of $2007$.
Izvor: Srednjoeuropska matematička olimpijada 2007, ekipno natjecanje, problem 8