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with 
.![\[
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be a positive integer. A positive integer 
is called a benefactor of if the positive divisors of can be partitioned into two sets 
and 
such that is equal to the sum of elements in minus the sum of the elements in . Note that or could be empty, and that the sum of the elements of the empty set is 
.
is a benefactor of 
because 
. has at least 
benefactors.
satisfying the following.
+1 w
in the plane of 
such that 
Let 
be the points of intersection of the medians of the triangles 
, respectively. Prove that the segments 
and 
are equal and have a common point.
in the plane of such that Let be the points of intersection of the medians of the triangles , respectively. Prove that the segments and are equal and have a common point.
and 
: Prove that :
