[/quote]
,
,
and
meaning 
is the least common multiple of the numbers 
.
such that
for every positive integer 
be positive integers with 
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,
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 
.
is mundane if there exist positive integers 
and 
less than 
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 
is a divisor of 
.
satisfy that: 
and natural number 
Y by jhu08
Suppose the points 
lie on the side 
and the points 
lie on the side 
of the right triangle 
(
) such that 
and 
. Let the lines 
and 
intersect at point 
. Find 
if it is known that 
.
lie on the side 
and the points 
lie on the side 
of the right triangle 
(
) such that 
and 
. Let the lines 
and 
intersect at point 
. Find 
if it is known that 
.This post has been edited 1 time. Last edited by parmenides51, Sep 13, 2021, 7:08 PM
Reason: typos corrected, see #3
Reason: typos corrected, see #3
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and 
?? It is the same angle.
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and chased every single angle but did not see how to proceed 
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