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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 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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Interesting inequality
sqing   1
N 33 minutes ago by Zok_G8D
Source: Own
Let $ a, b,c>0,b+c\geq 3a$. Prove that
$$ \sqrt{\frac{a}{b+c-a}}-\frac{ 2a^2-b^2-c^2}{(a+b)(a+c)}\geq \frac{2}{5}+\frac{1}{\sqrt 2}$$$$ \frac{3}{2}\sqrt{\frac{a}{b+c-a}}-\frac{ 2a^2-b^2-c^2}{(a+b)(a+c)}\geq \frac{2}{5}+\frac{3}{2\sqrt 2}$$
1 reply
sqing
Yesterday at 2:49 AM
Zok_G8D
33 minutes ago
J
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Basic ideas in junior diophantine equations
Maths_VC   6
N 36 minutes ago by Adywastaken
Source: Serbia JBMO TST 2025, Problem 3
Determine all positive integers $a, b$ and $c$ such that
$2$ $\cdot$ $10^a + 5^b = 2025^c$
6 replies
Maths_VC
May 27, 2025
Adywastaken
36 minutes ago
J
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$p|f(m+n) \iff p|f(m) + f(n)$ (IMO Shortlist 2007, N5)
orl   49
N 43 minutes ago by blueprimes
Source: IMO Shortlist 2007, N5, AIMO 2008, TST 3, P3
Find all surjective functions $ f: \mathbb{N} \to \mathbb{N}$ such that for every $ m,n \in \mathbb{N}$ and every prime $ p,$ the number $ f(m + n)$ is divisible by $ p$ if and only if $ f(m) + f(n)$ is divisible by $ p$.

Author: Mohsen Jamaali and Nima Ahmadi Pour Anari, Iran
49 replies
orl
Jul 13, 2008
blueprimes
43 minutes ago
J
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Inequality in triangle
Nguyenhuyen_AG   2
N an hour ago by JARP091
Let $a,b,c$ be the lengths of the sides of a triangle. Prove that
\[\frac{1}{(a-4b)^2}+\frac{1}{(b-4c)^2}+\frac{1}{(c-4a)^2} \geqslant \frac{1}{ab+bc+ca}.\]
2 replies
Nguyenhuyen_AG
4 hours ago
JARP091
an hour ago
J
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Interesting inequality
sqing   2
N an hour ago by sqing
Source: Own
Let $ a,b,c\geq 0 , a^2+b^2+c^2 =3.$ Prove that
$$ a^4+ b^4+c^4+6abc\leq9$$$$ a^3+ b^3+ c^3+3( \sqrt{3}-1)abc\leq 3\sqrt 3$$
2 replies
sqing
Today at 2:54 AM
sqing
an hour ago
J
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help me~~
Imshyso   1
N an hour ago by Royal_mhyasd
Given triangle ABC inscribed in (O) with orthocenter H. Let K be the midpoint of AH. Take E,F on AC, AB so that BKE=CKF=90. Prove that E,O,F are collinear.
1 reply
Imshyso
2 hours ago
Royal_mhyasd
an hour ago
J
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Isosceles Triangle Geo
oVlad   5
N 2 hours ago by Tamam
Source: Romania Junior TST 2025 Day 1 P2
Consider the isosceles triangle $ABC$ with $\angle A>90^\circ$ and the circle $\omega$ of radius $AC$ centered at $A.$ Let $M$ be the midpoint of $AC.$ The line $BM$ intersects $\omega$ a second time at $D.$ Let $E$ be a point on $\omega$ such that $BE\perp AC.$ Let $N$ be the intersection of $DE$ and $AC.$ Prove that $AN=2\cdot AB.$
5 replies
oVlad
Apr 12, 2025
Tamam
2 hours ago
J
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combinatorics problem
henderson   6
N 2 hours ago by aokmh3n2i2rt
$65$ distinct natural numbers not exceeding $2016$ are given. Prove that among these numbers we can find four $a,b,c,d$ such that $a+b-c-d$ is divisible by $2016.$
6 replies
henderson
Jan 23, 2016
aokmh3n2i2rt
2 hours ago
J
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Easy Geometry
rkm0959   13
N 2 hours ago by Rounak_iitr
Source: 2015 Korean Mathematical Olympiad P2
Let the circumcircle of $\triangle ABC$ be $\omega$. A point $D$ lies on segment $BC$, and $E$ lies on segment $AD$. Let ray $AD \cap \omega = F$. A point $M$, which lies on $\omega$, bisects $AF$ and it is on the other side of $C$ with respect to $AF$. Ray $ME \cap \omega = G$, ray $GD \cap \omega = H$, and $MH \cap AD = K$. Prove that $B, E, C, K$ are cyclic.
13 replies
rkm0959
Nov 1, 2015
Rounak_iitr
2 hours ago
J
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Find values for a, b ,c
Ferum_2710   2
N 3 hours ago by Jupiterballs
Source: Romania JBMO tst 2023 day2 p4
Let $M \geq 1$ be a real number. Determine all natural numbers $n$ for which there exist distinct natural numbers $a$, $b$, $c > M$, such that
$n = (a,b) \cdot (b,c) + (b,c) \cdot (c,a) + (c,a) \cdot (a,b)$
(where $(x,y)$ denotes the greatest common divisor of natural numbers $x$ and $y$).
2 replies
Ferum_2710
Apr 30, 2023
Jupiterballs
3 hours ago
J
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AIME qual outside US?
daijobu   10
N 5 hours ago by Yiyj
Can students outside the US take the AIME if they earn a qualifying score?
10 replies
daijobu
Yesterday at 7:10 PM
Yiyj
5 hours ago
J
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[$10K+ IN PRIZES] Poolesville Math Tournament (PVMT) 2025
qwerty123456asdfgzxcvb   20
N Today at 2:13 AM by panda2018
Hi everyone!

After the resounding success of the first three years of PVMT, the Poolesville High School Math Team is excited to announce the fourth annual Poolesville High School Math Tournament (PVMT)! The PVMT team includes a MOPper and multiple USA(J)MO and AIME qualifiers!

PVMT is open to all 6th-9th graders in the country (including rising 10th graders). Students will compete in teams of up to 4 people, and each participant will take three subject tests as well as the team round. The contest is completely free, and will be held virtually on June 7, 2025, from 10:00 AM to 4:00 PM (EST).

Additionally, thanks to our sponsors, we will be awarding approximately $10K+ worth of prizes (including gift cards, Citadel merch, AoPS coupons, Wolfram licenses) to top teams and individuals. More details regarding the actual prizes will be released as we get closer to the competition date.

Further, newly for this year we might run some interesting mini-events, which we will announce closer to the competition date, such as potentially a puzzle hunt and integration bee!

If you would like to register for the competition, the registration form can be found at https://pvmt.org/register.html or https://tinyurl.com/PVMT25.

Additionally, more information about PVMT can be found at https://pvmt.org

If you have any questions not answered in the below FAQ, feel free to ask in this thread or email us at falconsdomath@gmail.com!

We look forward to your participation!

FAQ
20 replies
qwerty123456asdfgzxcvb
Apr 5, 2025
panda2018
Today at 2:13 AM
J
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Expression is a Cube
nosaj   38
N Today at 1:42 AM by NicoN9
Source: 2015 AIME I Problem 3
There is a prime number $p$ such that $16p+1$ is the cube of a positive integer. Find $p$.
38 replies
nosaj
Mar 20, 2015
NicoN9
Today at 1:42 AM
J
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EGMO (geo) Radical Center Question
gulab_jamun   9
N Today at 12:58 AM by MathRook7817
For this theorem, Evan says that the power of point $P$ with respect to $\omega_1$ is greater than 0 if $P$ lies between $A$ and $B$. (I've underlined it). But, I'm a little confused as I thought the power was $OP^2 - r^2$ and since $P$ is inside the circle, wouldn't the power be negative since $OP < r$?
9 replies
gulab_jamun
May 25, 2025
MathRook7817
Today at 12:58 AM
J
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J
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Mop Qual stuff
HopefullyMcNats2025   65
N Apr 1, 2025 by fake123
How good of an award/ achievement is making MOP, I adore comp math but am scared if I dedicate all my time to it I won’t get in a good college such as MIT or Harvard
65 replies
HopefullyMcNats2025
Mar 30, 2025
fake123
Apr 1, 2025
J
Mop Qual stuff
G H J
Reveal topic tags
college apps
MIT
college
Harvard
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Mathandski
773 posts
Mathandski
#52 h  Mar 31, 2025, 9:34 PM • 1 Y
Y by cubres
idk about Harvard but from what I've seen, while MOP doesn't necessarily $\Longrightarrow$ MIT, doing math is arguably the most efficient use of time to get in MIT
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deduck
237 posts
deduck
#53 h  Mar 31, 2025, 9:56 PM • 1 Y
Y by cubres
fair but i think if ur only goal is colleges just do music competitions or smth because colleges wont think ur a big nerd and there isn't outrageous amounts of bribing/jury voting for their own students in the top competitions (which is basically the equivalent cheating like in math comps)
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cyberhacker
402 posts
cyberhacker
#54 h  Mar 31, 2025, 10:15 PM • 1 Y
Y by cubres
orangebear wrote:
I think the area you live in matters, For example if you are the only one in your entire school district to qualify for MOP then you'll most likely make MIT (unless your essays are dogwater), but if you go to a school where there are like 3-4 MOP qualifiers you stand out less.

on mit's website they specifically say that they look at you individually and you are not compared to anyone from your school, decision is entirely independent. some people may say that mit is lying and they just say that but i dont think a top tier college can afford to make such a big lie. and anyways mit is usually very open about admission questions, check their blogs.
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HungryCalculator
541 posts
HungryCalculator
#56 h  Mar 31, 2025, 11:41 PM • 1 Y
Y by cubres
Andyluo wrote:
over 95% of people who qualify to ivies don't make USAMO or USAJMO

I will use the above quote in this:
Correct me if I'm wrong:

A total of about 500 students qual for AMO and JMO together each year. According to this, https://www.forbes.com/sites/christopherrim/2025/03/28/the-results-are-in-here-are-ivy-league-and-top-college-admissions-rates-for-the-class-of-2029/, over 8,000+ students got excepted into the Ivies this year. 8,000 is a significant underestimate I'm sure, but we will still use it for this example to prove my point for the reality of there being more students accepted into the Ivies.

Given that over 95% percent of the people who get into ivies don't make USAMO or JMO, a maximum of 5% of total admits, or 400 admits at minimum have made USAMO or JMO,

Now, 400 out of 500 or 80% sounds great to me. 80% of JMO and AMO qualifiers (approx.) get into the Ivies.

So yeah, the main takeaways are that
1. JMO/AMO is absolutely not necessary to get into ivies (95% admits don't have it)
2. JMO/AMO significantly helps you get into the ivies (80% qualifiers have got in.)

Keep in mind, that there are more than 8000 admits, so this increases the percentage in number 2.

I disagree with those who say that JMO/AMO qual is not nearly enough by itself, because these stats disprove that.
However, there is most definitely more to the application that just one accomplishment.
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Pengu14
638 posts
Pengu14
#57 h  Mar 31, 2025, 11:46 PM • 1 Y
Y by cubres
@above those last two sentences are contradictory
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DottedCaculator
7357 posts
DottedCaculator
#58 h  Mar 31, 2025, 11:48 PM • 4 Y
Y by Pengu14, vincentwant, cubres, Exponent11
you flipped the inequality sign
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sadas123
1330 posts
sadas123
#60 h  Apr 1, 2025, 1:04 AM • 1 Y
Y by cubres
Did anyone here get accepted from Harvard?
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sadas123
1330 posts
sadas123
#61 h  Apr 1, 2025, 1:06 AM • 1 Y
Y by cubres
I only know 1 person or that is 2 I forgot.
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miguel00
601 posts
miguel00
#63 h  Apr 1, 2025, 2:07 AM • 1 Y
Y by cubres
xTimmyG wrote:
MOP is terrible for college applications. If you make MOP, you still have a high chance of being rejected from every college. My friend made MOP and got rejected from community college.

In the end, make MOP because you enjoy math.

Yeah you will get accepted with that stat unless you do something egregious...
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giratina3
556 posts
giratina3
#64 h  Apr 1, 2025, 2:33 AM • 1 Y
Y by cubres
jellybeanzzz wrote:
giratina3 wrote:
What I was trying to say was that most MIT students make MOP

there’s 4500 undergrads at MIT and you’re saying most of them made MOP?

oh my god bro this is so hard to say without getting flamed or roasted :skull:

dude, what I'm trying to say is that most MIT students DO some kind of math. basically all of them are JMO/AMO or MOP quals. I'm not saying ALL of them are. I'm saying most of them. Of course, duh, there are people who are EXTREMELY talented at sports get into MIT, but I'm not... bruh.. I give up
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Yiyj1
1268 posts
Yiyj1
#65 h  Apr 1, 2025, 2:39 AM • 1 Y
Y by cubres
giratina3 wrote:
jellybeanzzz wrote:
giratina3 wrote:
What I was trying to say was that most MIT students make MOP

there’s 4500 undergrads at MIT and you’re saying most of them made MOP?

oh my god bro this is so hard to say without getting flamed or roasted :skull:

dude, what I'm trying to say is that most MIT students DO some kind of math. basically all of them are JMO/AMO or MOP quals. I'm not saying ALL of them are. I'm saying most of them. Of course, duh, there are people who are EXTREMELY talented at sports get into MIT, but I'm not... bruh.. I give up

maybe u mean most mop students make mit?
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giratina3
556 posts
giratina3
#66 h  Apr 1, 2025, 2:40 AM • 1 Y
Y by cubres
yes @above, it is unbelievable what can happen if I switch the two :skull: :skull:
oh crap, wait I said that shoot i'll go fix it
This post has been edited 1 time. Last edited by giratina3, Apr 1, 2025, 2:41 AM
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mathboy282
2990 posts
mathboy282
#67 h  Apr 1, 2025, 2:41 AM • 4 Y
Y by cdm, cubres, aidensharp, vincentwant
Not to be a hypocrite but all of this is egregious advice considering none of y'all actually work in admissions.
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sadas123
1330 posts
sadas123
#69 h  Apr 1, 2025, 9:31 PM
Y by
fake123 wrote:
sadas123 wrote:
Not trying to be mean but if you do math comp for college you wont get into ivy leagues, mabye 1 or 2 but Ivy Leagues, the strat is that focus on ONE TOPIC DO NOT CHANGE IT START THAT IN MIDDLE SCHOOL. Pick what you want to do in 6th grade and do that for example scientists do science fair, mathematician, do math comp. Colleges like to see that you focus one one thing but you are dedicated to it and you can also perform good enough and mabye they will. MOP Qual doesn't garruntie anything and if you do it, it is for your own benefit, colleges focus more on your unique characteristics and your mood and what you do. They focus on your achievements that you focus that benefit the world and not you, for example getting 1st place doesn't gaurantee anything because if you do 6 different activities and get 3rd place state that Is worse than doing 1 thing and getting 1st place international. Attached below is a screenshot from the Harvard Website and check it out and you will learn exactly what you need to get into it. Harvard isn't the only school there are many other good colleges like Stanford, Duke, and many more. Just pour all your hard work into focusing on the thing that you love a lot. This is a prove trick which someone I know I can not say there name because of personal reasons, got into every Ivy League college and waitlisted from Harvard.

bro what ur acting like you already graduated ur in 6th grade middle school and high school is a time for exploration not relentless grinding achievements like your life is gonna end if you don't get into a good college

Who said I am 6th grade? what if I amn't what if I am actually in college what if I am in 2nd grade. :diablo:
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fake123
93 posts
fake123
#70 h  Apr 1, 2025, 10:49 PM
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u said u were in 6th grade
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