such that 
but 
does not divide 
.
and ![\[ 3n^2+3n+7=m^3 \]](http://latex.artofproblemsolving.com/6/f/8/6f84f81f857094b3ea432284a7881697167b2418.png)
be a point on the Neuberg cubic. Let the lines through 
respectively perpendicular to 
form a triangle 
.
Y by PikaPika999
Let 
be complex numbers such that
for any 
with 
Prove that
and 
for any 
be complex numbers such that
for any 
with 
Prove that
and 
for any 
This post has been edited 1 time. Last edited by Filipjack, Apr 6, 2025, 5:06 PM
![\(\eta:= \displaystyle\sum _{k\in[0,n]}\textstyle(\zeta_{n+1}^k)^{n-m}\left(\displaystyle\sum \textstyle a_i (\zeta_{n+1}^k)^i\right)=(n+1)a_m\)](http://latex.artofproblemsolving.com/9/1/0/910ac8f6d06849242b5c2d7af7d5ab9f634b0501.png)
,
.![\((n+1)\|a_m\|=\|\eta\|\le n+1\ \ \forall m\in[0,n]\)](http://latex.artofproblemsolving.com/4/c/4/4c412381cf65c5ba0576d7f5066c961a5cf3b3b3.png)
.
.
