[/quote]
,
be a sequence of positive integers with 
,
and![\[a_n = a_{n-1}^{a_{n-1}a_{n-2}}-1\]](http://latex.artofproblemsolving.com/1/b/f/1bf1a88979e7d2b33530de979d66a4e81032953d.png)
for all 
.
is a prime less than 
for some positive integer 
,
such that 
.
be a triangle with circumcircle 
,
.
,
,
with 
,
,
,
intersect at 
and lines 
and 
intersect at 
.
and 
intersect again at 
.
and 
intersect the circumcircle of triangle 
again at 
and 
,
lies on 
.
for which
(use in a problem for junior) to practice. Can anyone share to me?
be an acute angled scalene triangle with circumcircle 
.
and 
be the circumcenter and orthocenter of 
respectively. Let 
and 
be points on segments 
and 
Prove that 
and 
intersect on the circumcircle of 
.
grid with 
rows and 
columns, and each square of the grid is filled with a non-negative integer. Let 
be the average of all the numbers in the grid. Prove that if 
the there exist two identical rows (meaning same numbers in the same order).
is called feirense if it is possible to write on a sheet of paper some integers such that every positive divisor of 
be a square with 
side length and with center 
.
is drawn where point 
lies on line 
.
,
where 
is the number of times the number 
appears in the list. So, for example, for the list 
,
.
numbers. Then he asked him to apply the program to the resulting list, and so on, until a number greater than or equal to 
,
table is colored black or white. Every cell on table border is black. It is known, that in every 
square there are cells of two colors. Prove, that exist 
and 
are acute and 
.
,
.
Y by rama1728, David-Vieta, parmenides51
Hello everyone. Here are the problems from 2022 IMOC.
This year the camp was held from August 15 to August 21, but USJL was too busy to post the problems, so I posted them instead. Sorry for the big delay.
This year's shortlist has 6 problems in each category.
My English and LaTeX skill is not so proficient, so there may be errors. Tell me if you find any.
edit: the FE problems had been fixed.
edit: Fixed a minor typo in G2 and a severe typo in G3.
This year the camp was held from August 15 to August 21, but USJL was too busy to post the problems, so I posted them instead. Sorry for the big delay.
This year's shortlist has 6 problems in each category.
My English and LaTeX skill is not so proficient, so there may be errors. Tell me if you find any.
edit: the FE problems had been fixed.
edit: Fixed a minor typo in G2 and a severe typo in G3.
This post has been edited 2 times. Last edited by CrazyInMath, Sep 24, 2022, 1:47 PM
Reason: fixing typos
Reason: fixing typos
"
are collinear iff 
are concyclic
board with these pieces without gaps and overlaps. Determine the minimum number of 
pieces should be used to cover the whole board and not exceed the board. (There are an infinite number of these three types of pieces.)
)
