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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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have you done DCX-Russian?
GoodMorning   83
N 25 minutes ago by ray66
Source: 2023 USAJMO Problem 3
Consider an $n$-by-$n$ board of unit squares for some odd positive integer $n$. We say that a collection $C$ of identical dominoes is a maximal grid-aligned configuration on the board if $C$ consists of $(n^2-1)/2$ dominoes where each domino covers exactly two neighboring squares and the dominoes don't overlap: $C$ then covers all but one square on the board. We are allowed to slide (but not rotate) a domino on the board to cover the uncovered square, resulting in a new maximal grid-aligned configuration with another square uncovered. Let $k(C)$ be the number of distinct maximal grid-aligned configurations obtainable from $C$ by repeatedly sliding dominoes. Find the maximum value of $k(C)$ as a function of $n$.

Proposed by Holden Mui
83 replies
GoodMorning
Mar 23, 2023
ray66
25 minutes ago
J
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Four points are concyclic
DreamTeam   9
N 29 minutes ago by AylyGayypow009
Source: Moldova IMO-BMO TST 2003, day 1, problem 3
Let $ ABCD$ be a quadrilateral inscribed in a circle of center $ O$. Let M and N be the midpoints of diagonals $ AC$ and $ BD$, respectively and let $ P$ be the intersection point of the diagonals $ AC$ and $ BD$ of the given quadrilateral .It is known that the points $ O,M,Np$ are distinct. Prove that the points $ O,N,A,C$ are concyclic if and only if the points $ O,M,B,D$ are concyclic.

Proposer: Dorian Croitoru
9 replies
DreamTeam
Aug 14, 2008
AylyGayypow009
29 minutes ago
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cubefree divisibility
DottedCaculator   63
N 33 minutes ago by Assassino9931
Source: 2021 ISL N1
Find all positive integers $n\geq1$ such that there exists a pair $(a,b)$ of positive integers, such that $a^2+b+3$ is not divisible by the cube of any prime, and $$n=\frac{ab+3b+8}{a^2+b+3}.$$
63 replies
DottedCaculator
Jul 12, 2022
Assassino9931
33 minutes ago
J
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Titu Factoring Troll
GoodMorning   77
N 35 minutes ago by ray66
Source: 2023 USAJMO Problem 1
Find all triples of positive integers $(x,y,z)$ that satisfy the equation
$$2(x+y+z+2xyz)^2=(2xy+2yz+2zx+1)^2+2023.$$
77 replies
GoodMorning
Mar 23, 2023
ray66
35 minutes ago
J
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$n$ with $2000$ divisors divides $2^n+1$ (IMO 2000)
Valentin Vornicu   67
N an hour ago by alexanderchew
Source: IMO 2000, Problem 5, IMO Shortlist 2000, Problem N3
Does there exist a positive integer $ n$ such that $ n$ has exactly 2000 prime divisors and $ n$ divides $ 2^n + 1$?
67 replies
Valentin Vornicu
Oct 24, 2005
alexanderchew
an hour ago
J
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Hard Number Theory
MuradSafarli   1
N an hour ago by MR.1
Find all odd natural numbers \( m \) such that \( m^2 - 1 \mid 3^m + 5^m \).
1 reply
MuradSafarli
Yesterday at 7:06 PM
MR.1
an hour ago
J
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most bruh geo you can imagineeeeeeeeeeeeee
ItzsleepyXD   0
an hour ago
Source: bruhhhhhh
Let $ABC$ be triangle with $AC>AB$ and $B'$ on the segment $AC$ such that $AB=AB'$ . Consider point $E,F$ on $AB,AC$ such that $EF \parallel BB'$ . Point $T$ is the intersection of tangent line through point $E,F$ to circle $(EBC),(FBC)$ respectively . If the tangent through point $B'$ to $(BB'C)$ intersect $AB$ at $K$ . Line $KT$ intersect $BC$ at $D$ . Prove that $AD$ bisect $\angle BAC$ .
0 replies
ItzsleepyXD
an hour ago
0 replies
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x!+y!=x^y
Yimin Ge   10
N an hour ago by Assassino9931
Source: MEMO Individual Competition, Question 4
Determine all pairs $ (x,y)$ of positive integers satisfying the equation
\[ x!+y!=x^{y}.\]
10 replies
Yimin Ge
Sep 24, 2007
Assassino9931
an hour ago
J
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A final attempt to make a combinatorics problem
JARP091   4
N an hour ago by JARP091
Source: At the time of posting the problem I do not know the source if any
Let \( N \) be a positive integer and consider the set \( S = \{1, 2, \ldots, N\} \).

Two players alternate moves. On each turn, the current player must select a nonempty subset \( T \subseteq S \) of numbers not previously chosen such that for every distinct \( x, y \in T \), neither \( x \) divides \( y \) nor \( y \) divides \( x \).

After selecting \( T \), all multiples of every element in \( T \), including those in \( T \) itself, are removed from \( S \).

The game continues with the reduced set \( S \) until no moves are possible.
Determine, for each \( N \), which player has a winning strategy if any

Note: It might be wrong or maybe too easy.
4 replies
JARP091
2 hours ago
JARP091
an hour ago
J
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Less than or equal to 30°
orl   11
N an hour ago by Twan
Source: IMO 1991, Day 2, Problem 4, IMO ShortList 1991, Problem 24 (FRA 2)
Let $ \,ABC\,$ be a triangle and $ \,P\,$ an interior point of $ \,ABC\,$. Show that at least one of the angles $ \,\angle PAB,\;\angle PBC,\;\angle PCA\,$ is less than or equal to $ 30^{\circ }$.
11 replies
orl
Nov 11, 2005
Twan
an hour ago
J
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Simple Geometry
AbdulWaheed   4
N an hour ago by shanelin-sigma
Source: EGMO
Try to avoid Directed angles
Let ABC be an acute triangle inscribed in circle $\Omega$. Let $X$ be the midpoint of the arc $\overarc{BC}$ not containing $A$ and define $Y, Z$ similarly. Show that the orthocenter of $XYZ$ is the incenter $I$ of $ABC$.
4 replies
AbdulWaheed
Yesterday at 5:15 AM
shanelin-sigma
an hour ago
J
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Serbian selection contest for the IMO 2025 - P6
OgnjenTesic   1
N 2 hours ago by JARP091
Source: Serbian selection contest for the IMO 2025
For an $n \times n$ table filled with natural numbers, we say it is a divisor table if:
- the numbers in the $i$-th row are exactly all the divisors of some natural number $r_i$,
- the numbers in the $j$-th column are exactly all the divisors of some natural number $c_j$,
- $r_i \ne r_j$ for every $i \ne j$.

A prime number $p$ is given. Determine the smallest natural number $n$, divisible by $p$, such that there exists an $n \times n$ divisor table, or prove that such $n$ does not exist.

Proposed by Pavle Martinović
1 reply
OgnjenTesic
Thursday at 4:07 PM
JARP091
2 hours ago
J
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Need help with combi problems
JARP091   4
N 4 hours ago by JARP091
I want to create a problem set of some of the hardest combi problems that are yet to appear in any contest. Can anyone help me out? Also can anyone give me some tips to create combi problems.
4 replies
JARP091
Yesterday at 5:43 PM
JARP091
4 hours ago
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Essentially, how to get good at olympiad math?
gulab_jamun   12
N 4 hours ago by sagayao
Ok, so I'm posting this as an anynonymous user cuz I don't want to get flamed by anyone I know for my goals but I really do want to improve on my math skill.

Basically, I'm alright at computational math (10 AIME, dhr stanford math meet twice) and I hope I can get good enough at olympiad math over the summer to make MOP next year (I will be entering 10th as after next year, it becomes much harder :( )) Essentially, I just want to get good at olympiad math. If someone could, please tell me how to study, like what books (currently thinking of doing EGMO) but I don't know how to get better at the other topics. Also, how would I prepare? Like would I study both proof geometry and proof number theory concurrently or just study each topic one by one?? Would I do mock jmo/amo or js prioritize olympiad problems in each topic. I have the whole summer ahead of me, and intend to dedicate it to olympiad math, so any advice would be really appreciated. Thank you!
12 replies
gulab_jamun
May 18, 2025
sagayao
4 hours ago
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Question
HopefullyMcNats2025   19
N Apr 29, 2025 by MC_ADe
Is it more difficult to make MOP or make usajmo, usapho, and usabo
19 replies
HopefullyMcNats2025
Apr 7, 2025
MC_ADe
Apr 29, 2025
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Question
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Reveal topic tags
USA(J)MO
USAPhO
usabo
AMC
USAJMO
MOP
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G H BBookmark kLocked kLocked NReply
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#1 h  Apr 7, 2025, 2:00 AM
Y by
Is it more difficult to make MOP or make usajmo, usapho, and usabo
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#2 h  Apr 7, 2025, 2:02 AM
Y by
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
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ConfidentKoala4
611 posts
ConfidentKoala4
#3 h  Apr 7, 2025, 2:07 AM
Y by
all hard, usabo prolly easiest
mop prolly hardest
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HopefullyMcNats2025
45 posts
HopefullyMcNats2025
#4 h  Apr 7, 2025, 2:12 AM
Y by
Thanks man
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xHypotenuse
787 posts
xHypotenuse
#5 h  Apr 7, 2025, 4:44 PM • 3 Y
Y by happyhippos, aidan0626, Elephant200
No one cares about USABO/USAPhO is wild
This post has been edited 1 time. Last edited by xHypotenuse, Apr 7, 2025, 7:41 PM
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Ruegerbyrd
1105 posts
Ruegerbyrd
#6 h  Apr 7, 2025, 9:09 PM
Y by
MOP, USA(J)MO, usapho, usabo
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MC_ADe
183 posts
MC_ADe
#7 h  Apr 7, 2025, 9:16 PM
Y by
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
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TetraFish
1088 posts
TetraFish
#8 h  Apr 8, 2025, 12:47 AM
Y by
I think he means MOP vs making that stage in all 3 of them combined.
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LockingIN2026
5 posts
LockingIN2026
#9 h  Apr 8, 2025, 1:13 AM
Y by
TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

prob the latter
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elasticwealth
342 posts
elasticwealth
#10 h  Apr 8, 2025, 1:17 PM • 1 Y
Y by Sunhaops
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME
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NoSignOfTheta
1747 posts
NoSignOfTheta
#11 h  Apr 8, 2025, 1:25 PM
Y by
MC_ADe wrote:
u should talk about camping in these respective things instead cuz MOP is literally camping so u need to like say phys camp or bio camp not jst usapho or usabo
HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps
Z K Y
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sadas123
1319 posts
sadas123
#13 h  Apr 8, 2025, 8:37 PM
Y by
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

That is somewhat of the list.
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happyhippos
2199 posts
happyhippos
#14 h  Apr 8, 2025, 8:59 PM
Y by
HopefullyMcNats2025 wrote:
Btw Usabo and usapho no one cares, I mean usapho and usabo camps

That's an interesting thing to say, considering USAPhO-style physics is much more relevant to actually useful real-life things than USAMO-style math.
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mdk2013
644 posts
mdk2013
#15 h  Apr 8, 2025, 9:08 PM
Y by
fake123 wrote:
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

wdym qualifying for AMC 8 is harder

:ewpu: wut
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Jack_w
109 posts
Jack_w
#16 h  Apr 8, 2025, 9:55 PM
Y by
TetraFish wrote:
I think he means MOP vs making that stage in all 3 of them combined.

MOP harder
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nsking_1209
175 posts
nsking_1209
#17 h  Apr 9, 2025, 2:42 AM
Y by
MOP > usabo camp > usapho camp > usaco camp > usajmo
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Sunhaops
8 posts
Sunhaops
#18 h  Apr 29, 2025, 6:53 PM
Y by
elasticwealth wrote:
MOP >> USABO Camp > USAPhO Camp >>> USAMO Qual > JMO Qual >>> USAPhO qual / USABO Semifinal Qual > AIME

well said, only before AIME should be >> instead of >
This post has been edited 1 time. Last edited by Sunhaops, Apr 29, 2025, 6:54 PM
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xHypotenuse
787 posts
xHypotenuse
#19 h  Apr 29, 2025, 7:37 PM
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Not really, usapho qual isn't severely difficult compared to aime.

Also, I think usapho camp is around equal or harder than usabo camp for sure
This post has been edited 1 time. Last edited by xHypotenuse, Apr 29, 2025, 7:38 PM
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Lijin
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Lijin
#20 h  Apr 29, 2025, 10:19 PM
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I thought you had to make USA(J)MO first to make MOP?
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MC_ADe
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#21 h  Apr 29, 2025, 10:29 PM
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by usabo do u mean semifinals, camp or what
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