AoPS Wiki talk:Problem of the Day/September 6, 2011
Since , , so and since , .
If we were to have , then , which defies the first equation. Thus, . Since we must also have .
From there, we can simply test values. We know , so we test . It fails, since the maximum possible base, , has a sum of only 2046.
Testing , we see that works, so the minimum is .