IMO Shortlist 1984 problem 12
Dodao/la:
arhiva2. travnja 2012. Find one pair of positive integers
![a,b](/media/m/7/d/8/7d8bdace47e602448e6040957d8cf923.png)
such that
![ab(a+b)](/media/m/e/b/0/eb0476c5004dfc6215de43f5ad3e592f.png)
is not divisible by
![7](/media/m/5/1/9/519154d5119d15088eebb25b656d58dd.png)
, but
![(a+b)^7-a^7-b^7](/media/m/8/4/e/84ee592d657d3e8d92ac2652d9f551bc.png)
is divisible by
![7^7](/media/m/f/7/b/f7b9da575ee2a24c37c63656d7341412.png)
.
%V0
Find one pair of positive integers $a,b$ such that $ab(a+b)$ is not divisible by $7$, but $(a+b)^7-a^7-b^7$ is divisible by $7^7$.
Izvor: Međunarodna matematička olimpijada, shortlist 1984