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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
J
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Inequality
lgx57   9
N an hour ago by lgx57
Source: Own
$a,b,c>0,ab+bc+ca=1$. Prove that

$$\sum \sqrt{8ab+1} \ge 5$$
(I don't know whether the equality holds)
9 replies
lgx57
Saturday at 3:14 PM
lgx57
an hour ago
J
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old one but good one
Sunjee   2
N an hour ago by ehuseyinyigit
If $x_1,x_2,...,x_n $ are positive numbers, then prove that
$$\frac{x_1}{1+x_1^2}+\frac{x_2}{1+x_1^2+x_2^2}+\cdots+ \frac{x_n}{1+x_1^2+\cdots+x_n^2}\geq \sqrt{n}$$
2 replies
Sunjee
3 hours ago
ehuseyinyigit
an hour ago
J
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Inspired by giangtruong13
sqing   0
an hour ago
Source: Own
Let $ a,b>0 .$ Prove that$$ \frac{a}{b}+\frac{b}{a}+\frac{a^3}{2b^3+kab^2}+\frac{2b^3}{a^3+b^3+kab^2} \geq \frac{2k+7}{k+2}$$Where $ k\geq 0. $
0 replies
sqing
an hour ago
0 replies
J
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Functional equation
Math-wiz   24
N an hour ago by nmoon_nya
Source: IMOC SL A1
Find all functions $f:\mathbb{R}\to\mathbb{R}$ such that for all $x,y\in\mathbb{R}$,
$$f(xy+f(x))=f(xf(y))+x$$
24 replies
Math-wiz
Dec 15, 2019
nmoon_nya
an hour ago
J
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we can find one pair of a boy and a girl
orl   18
N 2 hours ago by bin_sherlo
Source: Vietnam TST 2001 for the 42th IMO, problem 3
Some club has 42 members. It’s known that among 31 arbitrary club members, we can find one pair of a boy and a girl that they know each other. Show that from club members we can choose 12 pairs of knowing each other boys and girls.
18 replies
orl
Jun 26, 2005
bin_sherlo
2 hours ago
J
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geometry
blug   0
2 hours ago
In trapezius $ABCD$, segments $AB$ and $CD$ are parallel. Angle bisectors of $\angle B$ and $\angle D$ intersect at $P$. Circumcircles of $ABP$ and $CDP$ meet again at $Q$. Angle bisector of $\angle D$ cuts $AB$ at $S$. Prove that
$$1. QD=QS,$$$$2. \angle DCQ=\angle BCQ,$$$$3. \angle BAQ=\angle QAD.$$
0 replies
blug
2 hours ago
0 replies
J
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Eulerline problem
Retemoeg   0
2 hours ago
Source: Extension from a problem I read in a book
Show that the isogonal conjugate of the isotomic conjugate of the orthocenter lies on the Euler line.
0 replies
Retemoeg
2 hours ago
0 replies
J
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Inequality
MathsII-enjoy   6
N 2 hours ago by MathsII-enjoy
A interesting problem generalized :-D
6 replies
MathsII-enjoy
Saturday at 1:59 PM
MathsII-enjoy
2 hours ago
J
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Polynomial FE
MSTang   55
N 2 hours ago by P162008
Source: 2016 AIME I #11
Let $P(x)$ be a nonzero polynomial such that $(x-1)P(x+1)=(x+2)P(x)$ for every real $x$, and $\left(P(2)\right)^2 = P(3)$. Then $P(\tfrac72)=\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.
55 replies
MSTang
Mar 4, 2016
P162008
2 hours ago
J
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Number Theory
fasttrust_12-mn   8
N 2 hours ago by ErTeeEs06
Source: Pan African Mathematics Olympiad P1
Find all positive intgers $a,b$ and $c$ such that $\frac{a+b}{a+c}=\frac{b+c}{b+a}$ and $ab+bc+ca$ is a prime number
8 replies
fasttrust_12-mn
Aug 15, 2024
ErTeeEs06
2 hours ago
J
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My Unsolved FE on R+
ZeltaQN2008   4
N 2 hours ago by mashumaro
Source: IDK
Give $a>0$. Find all funcitions $f:\mathbb{R}^+ \rightarrow \mathbb{R}^+$ such that for all any $x,y\in (0,\infty):$
$$f(xf(y)+a)=yf(x+y+a)$$
4 replies
ZeltaQN2008
4 hours ago
mashumaro
2 hours ago
J
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purple comet discussion
ConfidentKoala4   59
N 4 hours ago by hzbrl
when can we discuss purple comet
59 replies
ConfidentKoala4
May 2, 2025
hzbrl
4 hours ago
J
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USAJMO problem 3: Inequality
BOGTRO   104
N Today at 4:00 AM by justaguy_69
Let $a,b,c$ be positive real numbers. Prove that $\frac{a^3+3b^3}{5a+b}+\frac{b^3+3c^3}{5b+c}+\frac{c^3+3a^3}{5c+a} \geq \frac{2}{3}(a^2+b^2+c^2)$.
104 replies
BOGTRO
Apr 24, 2012
justaguy_69
Today at 4:00 AM
J
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2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   68
N Today at 3:51 AM by RainbowSquirrel53B
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary

Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


68 replies
audio-on
Jan 26, 2025
RainbowSquirrel53B
Today at 3:51 AM
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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
Z K Y
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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
606 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
777 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
Z K Y
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Ruegerbyrd
1080 posts
Ruegerbyrd
#6 h  Apr 7, 2025, 9:09 PM
Y by
MOP, USA(J)MO, usapho, usabo
Z K Y
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MC_ADe
182 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
Z K Y
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elasticwealth
339 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
Z K Y
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NoSignOfTheta
1729 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
1262 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.
Z K Y
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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.
Z K Y
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mdk2013
638 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
Z K Y
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nsking_1209
171 posts
nsking_1209
#17 h  Apr 9, 2025, 2:42 AM
Y by
MOP > usabo camp > usapho camp > usaco camp > usajmo
Z K Y
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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
777 posts
xHypotenuse
#19 h  Apr 29, 2025, 7:37 PM
Y by
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
222 posts
Lijin
#20 h  Apr 29, 2025, 10:19 PM
Y by
I thought you had to make USA(J)MO first to make MOP?
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MC_ADe
182 posts
MC_ADe
#21 h  Apr 29, 2025, 10:29 PM
Y by
by usabo do u mean semifinals, camp or what
Z K Y
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