,
is the midpoint of 
and 
is a point on the side 
.
,
,
are positive integers 
.
is also an integer and equals 
.
,
such that for all positive real numbers 
and 
:
and 
be two isogonal conjugate with respect to triangle 
and 
be two points lying on the circle 
such that 
and 
are perpendicular and parallel to bisector of 
and 
bisect two arcs 
and not containing 
.
and 
.
of triangle 
.
be the reflection of 
be the foot of the perpendicular from 
,
be the midpoint of the segment 
.
intersect the circle 
.
is tangent to the circumcircle of triangle 
.
Y by kiyoras_2001
Problem. Let 
be the nonnegative integers in 
where 
. Define 
. Prove that 
.
Bonus problem (Open). Can we prove a tighter result than the one above? That is, is there a function
such that 
where 
, and the statement is still true when 
?
Or, is there a function such that 
where 
, and the statement is still true when ?.
be the nonnegative integers in 
where 
. Define 
. Prove that 
.Bonus problem (Open). Can we prove a tighter result than the one above? That is, is there a function
such that 
where 
, and the statement is still true when 
?Or, is there a function
such that 
where 
, and the statement is still true when ?.This post has been edited 10 times. Last edited by CBMaster, Apr 27, 2025, 5:43 AM
Reason: .
Reason: .
