[/quote]
,
is described on a circle 
,
be 
respectively. A circle with a center 
,
and lines 
.
,
and lines 
.
,
and lines 
,
and lines 
are concurrent.
such that 
is a divisor of 
.
,
and 
.
is prime, 
with 
and 
.
and 
are such that 
is a multiple of 
and 
is a multiple of 
be positive integers with 
.
,
,
,
,
,
positions to the right. Andrés and Beto alternate turns, starting with Andrés. The winner is the player who moves a token into the rightmost cell. Determine who has a winning strategy in terms of 
is mundane if there exist positive integers 
such that 
is a positive integer. Find, with proof, all prime numbers that are not mundane.
that has the following property: Any 
real numbers, not necessarily distinct, that lie in the interval ![$[100,101]$](http://latex.artofproblemsolving.com/8/e/3/8e3fe24e3b899bbf2128eebe08756e1ff963aaa0.png)
,
and 
such that
.
, 
and 
.
.
satisfy that: 
and natural number 
Y by Adventure10, Mango247
In a triangle 
, let 
and 
the atlitudes. Let 
be the point where the inner bisector of 
cuts to the side 
and 
is the distance from the point next to 
. The distances 
and 
are similarly defined. Show that:
For what kind of triangles does the equality hold?
, let 
and 
the atlitudes. Let 
be the point where the inner bisector of 
cuts to the side 
and 
is the distance from the point next to 
. The distances 
and 
are similarly defined. Show that:
For what kind of triangles does the equality hold?This post has been edited 3 times. Last edited by parmenides51, Dec 4, 2021, 8:34 PM
