AoPS Wiki talk:Problem of the Day/June 10, 2011
Problem
AoPSWiki:Problem of the Day/June 10, 2011
Solution
,
.
If
is an integer,
.
If
isn't an integer,
.
Since
or
,
or
. Checking all our solutions, they all work. Thus the solutions are
,
, or
, and the sum of them all is
.