[/quote]
,
,
be the least prime that does not divide 
,
to be the product of all primes less than 
For 
,
.
defined by 
and ![\[ x_{n+1} = \frac{x_n p(x_n)}{q(x_n)} \]](http://latex.artofproblemsolving.com/8/2/5/825be3bbef6a29de69aead03392ca7215093f320.png)
for 
.
such that 
.
be an infinite, nonconstant sequence of rational numbers, meaning it is not the case that 
Suppose that 
is also an infinite, nonconstant sequence of rational numbers with the property that 
is an integer for all 
and 
.
such that 
and 
are integers for all 
,
,
be an infinite sequence of positive integers. Suppose that there is an integer 
such that, for each 
,
is an integer. Prove that there is a positive integer 
such that 
for all 
.
be a right triangle with 
.
lies on the line 
such that 
is between 
.
be the midpoint of 
and let 
be the seconf intersection point of the circumcircle of 
and the circumcircle of 
.
passes through a fixed point.
and 
intersect each other at 
and 
.
and 
respectively. Let 
and 
be the reflection of 
intersect circles 
and 
(both distinct from 
is the second tangent to 
to 
face-down on a table. On each move, the Detective can point to two cards and inquire if the numbers on them are consecutive. The Magician replies truthfully. After a finite number of moves, the Detective points to two cards. She wins if the numbers on these two cards are consecutive, and loses otherwise.
questions.
= 2∠AMP.
is the midpoint of the arc 
,
,
,
be the 
intersects 
.
is perpendicular to 
,
is the incenter of 
and the circle 
of radius 
centered at 
Let 
The line 
intersects 
Let 
Let 
be the intersection of 
and 
to 
is a sequence of roads such that one can move from 
and 
denote the maximal number of paths in a diverse collection of paths from 
denote the maximal number of paths in a diverse collection of paths from 
holds if and only if the number of roads going out from 
Y by
Is there a rough difficulty comparison between IMO shortlist questions and USAMO questions? For example,
SL 1, 2, 3 -> USAMO P1
SL 4, 5, 6 -> USAMO P2
SL 7, 8, 9 -> USAMO P3
(This is just my guess; probably not correct)
Also feel free to compare it with other competitions(like the jmo) as well!
SL 1, 2, 3 -> USAMO P1
SL 4, 5, 6 -> USAMO P2
SL 7, 8, 9 -> USAMO P3
(This is just my guess; probably not correct)
Also feel free to compare it with other competitions(like the jmo) as well!
