,
?
be a positive integer such that ![\[
1 + \sum_{i=1}^{n-1} i^{n-1}.
\]](http://latex.artofproblemsolving.com/e/2/d/e2daf7800da3f984cd761ed1fecf10083444db25.png)
Prove that 
Y by
Let 
and 
be positive integers. For a connected simple graph 
on vertices and edges, we consider the number 
of orientations of (all of) its edges so that, in the resulting directed graph, every vertex has even outdegree.
Show that only depends on and , and determine its value.
and 
be positive integers. For a connected simple graph 
on vertices and edges, we consider the number 
of orientations of (all of) its edges so that, in the resulting directed graph, every vertex has even outdegree.Show that
only depends on and , and determine its value.
.
