[/quote]
,
be the orthocenter of acute triangle 
,
be the foot of the altitude from 
to 
,
be the reflection of 
.
intersects line 
and 
.
.
such that 
is an integer for every positive integer 
.
be a point on side 
such that 
.
be the circumcenter of 
,
satisfying 
.
.
,
,
,
jump is equal to 
.
over all pairs of positive integers 
.
lamps 
arranged in a circle in that order. At any given time, each lamp is either on or off. Every second, each lamp undergoes a change according to the following rule:
,
have the same state in the previous second, then 
which is on. Prove that for infinitely many integers 
and 
,
[list=a]
and 
,
satisfying this equation.
denotes the greatest common divisor of positive integers 
and 
for which there exist real numbers 
satisfying 
,
and
for 
.
such that 
holds for all positive rational numbers 
.
and 
.
Equality holds when 
Equality holds when 
or 
for some prime 
.
and 
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The Mathematical Association of America (MAA) is searching for a new Academic Director for the U.S. Math Olympiad Program (MOP) summer camp, who will also serve as the Team Leader of the U.S. IMO team starting in 2024. I am on the MAA's search committee to help them fill this position.
I have attached the MAA's announcement with details about the position and how to apply. (This announcement is also on the MAA's website.) If you know anyone who you think might be interested, please feel free to pass this announcement along to them.
I have attached the MAA's announcement with details about the position and how to apply. (This announcement is also on the MAA's website.) If you know anyone who you think might be interested, please feel free to pass this announcement along to them.
