[/quote]
,
for which the following statement is true: If positive integers 
and 
are such that 
is a multiple of 
and 
is a multiple of 
and
meaning 
is the least common multiple of the numbers 
.
such that
for every positive integer 
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 
.
,
on side 
.
passing through 
at point 
.
and 
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 
.
.
-
board.
board consisting of 
unit segments. A configuration of several 
satisfy that: 
and natural number 
Y by
Suppose 
is a regular tetrahedron with edge of the length 
. Through an interior point of face 
three planes are drawn parallel to faces 
and 
respectively. These planes split the tetrahedron in several parts. Find the total sum of the lengths of the edges of the part that contains vertex 
.
is a regular tetrahedron with edge of the length 
. Through an interior point of face 
three planes are drawn parallel to faces 
and 
respectively. These planes split the tetrahedron in several parts. Find the total sum of the lengths of the edges of the part that contains vertex 
.
