[/quote]
,
(i dont remember exactly if it was 8032038 or some other number, so correct me on this)
(i posted this at 12:29) lol
?
with 
and 
.
and 
intersect at 
,
and 
intersect at 
.
be the midpoints of sides 
,
and 
be points on segment 
and 
,
is the angle bisector of 
and 
is the angle bisector of 
.
is parallel to 
if and only if 
divides 
a point in the space and 
the centroid of a tetrahedron 
and 
be positive integers. If 
is divisible by 
for every positive integer 
,
.
of positive integers with the following property: all of the terms of the sequence 
have a greatest common divisor 
,
,
be nonzero real numbers such that 
and 
.
.
be non-negative real numbers such that ![\[b+c\leqslant a+1,\quad c+a\leqslant b+1,\quad a+b\leqslant c+1.\]](http://latex.artofproblemsolving.com/b/9/e/b9e86e898c0536b7323a03611d5bdbf679caa710.png)
Prove that 
be a function satisfying
for all integers 
and 
for all integers 
such that ![\[f(xy-1)+f(x)f(y)=2xy-1,\]](http://latex.artofproblemsolving.com/8/8/8/888ca39f2b7f8cec6d6426bee28d40eade40a66e.png)
for any real numbers 
and 
of positive integers with 
prime, 
,
,
is a multiple of 
.
be a 
makes a fixed angle with the tangent to 
be a rectangular hyperbola centered at the origin, scaled such that it is tangent to the logarithmic spiral at some point.
on the spiral, the polar of 
Y by Tem8, smbellanki, Skillfulcotton, aops-g5-gethsemanea2, happypi31415, Rounak_iitr, chewkokwah, anantmudgal09
Hi,
As part of my work with my country’s national olympiad system, I am developing a public resource guide on math contests. This guide covers every stage of contest participation, from complete beginners to those aiming for the highest levels of the USAMO and IMO.
I would be grateful for any feedback; if you have additional resource suggestions, please share them in this thread or by AoPS DM to foster discussion. I also particularly welcome comments as to whether a resource may be under/over-classified in the guide.
The following is the leveling system used, aligned with the corresponding tiers of the US contest framework. Note that the guide indicates the suggested practice contest or textbook for someone aspiring to reach the corresponding level, not someone currently at that level.
J: Strong middle-school student with little math exposure outside the curriculum
1A: Strong high-school student with little math exposure outside the curriculum, or Middle-school student scoring 20-35 at Mathcounts chapter
1B: AMC8* Honor Roll, AMC10 score of ~60-70
2A: AMC8 Distinguished HR, AMC10 score of ~80-90
2B: AIME qualifier (through either AMC10/12), AMC10 Honor Roll
3A: AMC10 Distinguished HR, AMC12 HR
3B: AMC12 Distinguished HR, USAJMO/USAMO Qualifier
4A: USAJMO Honorable Mention, USAMO ~50th percentile
4B: USAJMO Honors, USAMO Bronze, Red/Green MOP Cutoff
5A: USAJMO Top Honors, USAMO Silver, Blue MOP/TST Group Cutoff
5B: USAMO Gold, USAMO RMM/IMO team selection
As part of my work with my country’s national olympiad system, I am developing a public resource guide on math contests. This guide covers every stage of contest participation, from complete beginners to those aiming for the highest levels of the USAMO and IMO.
I would be grateful for any feedback; if you have additional resource suggestions, please share them in this thread or by AoPS DM to foster discussion. I also particularly welcome comments as to whether a resource may be under/over-classified in the guide.
The following is the leveling system used, aligned with the corresponding tiers of the US contest framework. Note that the guide indicates the suggested practice contest or textbook for someone aspiring to reach the corresponding level, not someone currently at that level.
J: Strong middle-school student with little math exposure outside the curriculum
1A: Strong high-school student with little math exposure outside the curriculum, or Middle-school student scoring 20-35 at Mathcounts chapter
1B: AMC8* Honor Roll, AMC10 score of ~60-70
2A: AMC8 Distinguished HR, AMC10 score of ~80-90
2B: AIME qualifier (through either AMC10/12), AMC10 Honor Roll
3A: AMC10 Distinguished HR, AMC12 HR
3B: AMC12 Distinguished HR, USAJMO/USAMO Qualifier
4A: USAJMO Honorable Mention, USAMO ~50th percentile
4B: USAJMO Honors, USAMO Bronze, Red/Green MOP Cutoff
5A: USAJMO Top Honors, USAMO Silver, Blue MOP/TST Group Cutoff
5B: USAMO Gold, USAMO RMM/IMO team selection
This post has been edited 4 times. Last edited by Konigsberg, Jan 28, 2025, 8:07 AM
