Prove that
of the pizza, where 
is a positive integer. Find 
![\[\mathcal{P}(x) = x^{108}+x^{102}+x^{96}+2x^{54}+3x^{36}+4x^{24}+5x^{18}+6\]](http://latex.artofproblemsolving.com/e/b/2/eb28918359848dd07784a3c2c6a34b934743c016.png)
be 
.![\[\dfrac{r_1^6+r_2^6+\dots+r_{108}^6}{r_1^6r_2^6+r_1^6r_3^6+\dots+r_{107}^6r_{108}^6}\]](http://latex.artofproblemsolving.com/3/1/5/315341a7adf35bc04e40ee0685a011c9f7b76115.png)
without Newton Sums.
and 
Prove that
high-quality questions. This test was created by multiple 130+ scorers, and we have tried our very best to produce the highest quality test possible. We've blended the question types in a good distribution, and maintained a realistic difficulty. (something most AOPS mocks fail at)
be the set of positive real numbers. Find all functions 
such that, for all 
,
Y by
Let 
be a rectangular parallelepiped and 
projections of points 
and 
respectively on the diagonal 
.
a) Prove that
.
b) Prove that
if and only if is a cube.
be a rectangular parallelepiped and 
projections of points 
and 
respectively on the diagonal 
.a) Prove that
.b) Prove that
if and only if is a cube.This post has been edited 1 time. Last edited by parmenides51, Aug 15, 2024, 7:51 AM
