[/quote]
,
.
![$P\in \mathbb{R}[x] $](http://latex.artofproblemsolving.com/1/1/9/1194a1382b5ae7a9945cf8d9a6281954cf8cdb3d.png)
with even-degree
be a real numbers such that 
P
Where 
be a cyclic quadrilateral with 
and let 
and 
be the feet of altitudes from 
to the lines 
and 
,
bisects 
.
is strictly increasing : 
,
be the set of positive integers that do not exceed 
as the smallest positive integer that allows 
satisfying 
,
,
.
P
Where 
be the set of 
with 
.
and 
such that
is a prime number.
be the midpoint of the side 
of triangle 
.
intersects the side 
.
intersect the lines 
and 
in 
and 
respectively. If the midpoint of 
is 
,
.
and 
?
and that the circumcircles of triangles 
and 
are tangent to each other. The line through 
,
and 
and let 
be the incenter of triangle 
.
.
Y by internationalnick123456
Is it possible to color all lattice points in plane into 3 colors such that
1. every line passing through lattice points and parallel to x axis has these three colors infinitely many(that is, every color appears infinitely many times in those lines).
2. every line passing through lattice points and not parallel to x axis cannot have three different color lattice points on it.
I think the answer is yes, but I couldn't find an example...
1. every line passing through lattice points and parallel to x axis has these three colors infinitely many(that is, every color appears infinitely many times in those lines).
2. every line passing through lattice points and not parallel to x axis cannot have three different color lattice points on it.
I think the answer is yes, but I couldn't find an example...
This post has been edited 5 times. Last edited by CBMaster, Apr 11, 2025, 6:58 PM
Reason: .
Reason: .
