such that ![$$\left(a^{3}+b^{3}+c^{3}-3abc\right)^{2}-\left[a^{3}+b^{3}+c^{3}+3abc-ab(a+b)-bc(b+c)-ca(c+a)\right]^{2}\ge 2k\cdot(a-b)^{2}(b-c)^{2}(c-a)^{2}$$](http://latex.artofproblemsolving.com/d/2/4/d24b46e65a587fbd977467b6e4e31838a0eb57aa.png)
forall 
such that p is a prime, 
and 
is a divisor of 
.
such that![\[ \frac {2^n + 1}{n^2}
\]](http://latex.artofproblemsolving.com/9/2/2/922444e7669c326efcad5fde3ea00f8c2d9fa5d8.png)
is an integer.
Y by
In a star-shaped closed broken line 
, 
meets 
and 
at 
and 
, 
meets and 
at 
and 
, and meets at 
, respectively, and 
. Prove that 
.
, 
meets 
and 
at 
and 
, 
meets and 
at 
and 
, and meets at 
, respectively, and 
. Prove that 
.
