holds 
.
with![\[2x^3zf(z)+yf(y) \ge 3yz^2f(x)\]](http://latex.artofproblemsolving.com/a/b/f/abf10d7e679f6f04db556424a0a0eda26f371fd4.png)
for all 
.
.
be a function taking in positive integers and outputting nonnegative integers, defined as follows:
is the number of positive integers 
with 
such that the equation 
has an integer solution 
.
such tha
Adit Aggarwal, India.
Y by Adventure10, Mango247
Point 
is taken on side 
of a triangle 
such that the centroid 
of triangle 
lies on the circumcircle of 
and the centroid 
of lies on the circumcircle of 
. Prove that the medians of the triangles and 
from are of the same length.
is taken on side 
of a triangle 
such that the centroid 
of triangle 
lies on the circumcircle of 
and the centroid 
of lies on the circumcircle of 
. Prove that the medians of the triangles and 
from are of the same length.
is the middle point of 
