such that ![\[f(2x+y) + f(x+f(2y)) = f(x)f(y) - xy\]](http://latex.artofproblemsolving.com/0/6/2/0623b7c328af6d088cfc5dd288afe3e17a94ff29.png)
for all reals 
and 
.
and 
be two sequences of integers such that 
and 
for all 
.
divides 
for an infinity of integers 
such that 
for all 
are coprime. Consider the sequence 
given by 
.
such that 
is even and 
is an integer. Prove that the numerator in its simplest form of 
is an odd integer greater than 
.
be an integer and let 
be 
distinct subsets of 
.
such that the n subsets 
are also disjoint.
s
.
Y by Adventure10, Mango247
In tetrahedron 
, 
and 
are barycenters of the faces 
and 
respectively.
(a) Prove that the straight lines
and 
are concurrent.
(b) Knowing that
and 
compute the maximum possible value of the volume of .
, 
and 
are barycenters of the faces 
and 
respectively.(a) Prove that the straight lines
and 
are concurrent.(b) Knowing that
and 
compute the maximum possible value of the volume of .
