from the set of non-negative integers to itself such that 
,
,
.
be the set of real numbers. Let 
be a function such that ![\[f(x+y)f(x-y)\geqslant f(x)^2-f(y)^2\]](http://latex.artofproblemsolving.com/5/d/3/5d3476fd9195d085d0030d6036a9fde1cf6756a7.png)
for every 
.
.
for every 
or 
for every 
be an integer. Ion draws a regular 
-
such that 
coprime, 
and 
.
Y by
Let 
, 
, 
are pairwise distinct real numbers satisfying 
Prove that
Let , , are pairwise distinct real numbers satisfying 
Prove that
, 
, 
are pairwise distinct real numbers satisfying 
Prove that
Let , , are pairwise distinct real numbers satisfying 
Prove that
This post has been edited 2 times. Last edited by sqing, Apr 24, 2025, 12:28 PM
Prove that
Where 
![\[
\begin{aligned}
(x - y)(x + y) &= z - y \\
(y - z)(y + z) &= y - x \\
(z - x)(z + x) &= x - z
\end{aligned}
\]](http://latex.artofproblemsolving.com/a/9/9/a997d3d3105ad7470627a4a2d82dbbfe16ae9dea.png)
