IMO Shortlist 1984 problem 3
Dodao/la:
arhiva2. travnja 2012. Find all positive integers
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
such that
![n=d_6^2+d_7^2-1,](/media/m/a/8/c/a8cb53463e940e877531fc4add889d45.png)
where
![1 = d_1 < d_2 < \cdots < d_k = n](/media/m/0/a/8/0a895d52c8cc8ea83d1c07b324e18cba.png)
are all positive divisors of the number
%V0
Find all positive integers $n$ such that
$$n=d_6^2+d_7^2-1,$$
where $1 = d_1 < d_2 < \cdots < d_k = n$ are all positive divisors of the number $n.$
Izvor: Međunarodna matematička olimpijada, shortlist 1984