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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 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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U.S.J.A.M.O tips from a superstar!
K-Cliquey   17
N 4 minutes ago by MrMustache
Source: smart people
Hi every body. I know it is very stressful because the U.S.J.A.M.O. is soon, I just want to make sure everyone pays attention to their mental health. Every day, remember mental health is more important than U.S.J.A.M.Ο.

And I used to be worse than my friend at U.S.J.A.M.O., but I improve, so here are my tips for making sure mental health on the U.S.J.A.M.O.


1. Drink water. You are not cactus.


2. Don't drink too much water. Or else you will pee.


3. Get protein. I recommend cow meat.


4. (I am serious) Have a girlfriend or a boyfriend. I got rejected 8 times before I met Lennon Court, but he is my best emotional support on the U.S.J.A.M.O. now. It is good emotional support.


5. Sleep early. I know you guys are scared of dreaming about bad U.S.J.A.M.O. grade, but just think about #4 so you can get mental healthy from sleep instead of nightmare.


6. Social to your friends! They are also good mental healthy support.



Now, most importantly, ADD YOUR TIPS TO THIS LIST. PLEASE COMMENT DOWN BELOW YOUR TIPS FOR GOOD MENTAL HEALTH. We are a TEAM to have good MENTAL HEALTH.
17 replies
K-Cliquey
Today at 4:56 AM
MrMustache
4 minutes ago
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Oi! These lines concur
Rg230403   17
N 18 minutes ago by L13832
Source: LMAO 2021 P5, LMAOSL G3(simplified)
Let $I, O$ and $\Gamma$ respectively be the incentre, circumcentre and circumcircle of triangle $ABC$. Points $A_1, A_2$ are chosen on $\Gamma$, such that $AA_1 = AI = AA_2$, and point $A'$ is the foot of the altitude from $I$ to $A_1A_2$. If $B', C'$ are similarly defined, prove that lines $AA', BB'$ and $CC'$ concurr on $OI$.
Original Version from SL
Proposed by Mahavir Gandhi
17 replies
Rg230403
May 10, 2021
L13832
18 minutes ago
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Find the period
Anto0110   1
N 22 minutes ago by Anto0110
Let $a_1, a_2, ..., a_k, ...$ be a sequence that consists of an initial block of $p$ positive distinct integers that then repeat periodically. This means that $\{a_1, a_2, \dots, a_p\}$ are $p$ distinct positive integers and $a_{n+p}=a_n$ for every positive integer $n$. The terms of the sequence are not known and the goal is to find the period $p$. To do this, at each move it possible to reveal the value of a term of the sequence at your choice.
If $p$ is one of the first $k$ prime numbers, find for which values of $k$ there exist a strategy that allows to find $p$ revealing at most $8$ terms of the sequence.
1 reply
Anto0110
Yesterday at 7:37 PM
Anto0110
22 minutes ago
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inequality
senku23   2
N an hour ago by User21837561
Let x,y,z in R+ prove that 8(x^3+y^3+z^3)2≥9(x^2+yz)(y^2+zx)(z^2+xy).
2 replies
senku23
2 hours ago
User21837561
an hour ago
J
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Differentiable functional
bakerbakura   2
N an hour ago by Gryphos
Find all differentiable functions $ f;\mathbb{R}\to\mathbb{R}$ such that, for all real numbers $ a,b,t$ with $ 0<t<1$, $ t^2f(a)+(1-t^2)f(b)\geq f(ta+(1-t)b)$
2 replies
bakerbakura
Jan 11, 2010
Gryphos
an hour ago
J
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function equation
cipher703516247   2
N an hour ago by luutrongphuc

Find all the functions $f: \mathbb R^{+} \to \mathbb R^{+}$such that:
$$f(xy^n +f(y)^{2n}) )=f(x)f(y)^n +(yf(y))^n $$
2 replies
cipher703516247
Feb 14, 2025
luutrongphuc
an hour ago
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gcd (a^n+b,b^n+a) is constant
EthanWYX2009   78
N an hour ago by SimplisticFormulas
Source: 2024 IMO P2
Determine all pairs $(a,b)$ of positive integers for which there exist positive integers $g$ and $N$ such that
$$\gcd (a^n+b,b^n+a)=g$$holds for all integers $n\geqslant N.$ (Note that $\gcd(x, y)$ denotes the greatest common divisor of integers $x$ and $y.$)

Proposed by Valentio Iverson, Indonesia
78 replies
EthanWYX2009
Jul 16, 2024
SimplisticFormulas
an hour ago
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Maximum Cost of Identifying Two Digits in a Three-Digit Number
Borisaurus   0
an hour ago
Source: 2025 MBL QQ P7 Variant
You find yourself on a flight to Bosnia and Herzegovina. You are seated next to a strange man wearing a hat—similar to the one worn by Indiana Jones. The man spends most of the flight rambling about some pyramids.

However, as you approach your destination, he tells you the following:

"I have thought of a $three-digit$ number. I will allow you to ask me questions. A question consists of you saying a three-digit number, to which I respond 'yes' if at least two of its digits are correct, or 'no' otherwise. (A digit is correct if it matches the corresponding digit in my number.)

You can ask as many questions as you like, but they come at a price. The game ends when you have correctly identified two digits of my number. If
you guess correctly, I will sell you my precious pyramid. You will have to pay a number of Bosnian marks equal to the number of questions you asked.

What is the maximum number of Bosnian marks you will have to pay using the best strategy?"
0 replies
Borisaurus
an hour ago
0 replies
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BMN is equilateral iff rectangle ABCD is square
parmenides51   3
N 2 hours ago by Tsikaloudakis
Source: 2004 Romania NMO SL - Shortlist VII-VIII p8 https://artofproblemsolving.com/community/c3950157_
Consider a point $M$ on the diagonal $BD$ of a given rectangle $ABCD$, such that $\angle AMC = \angle CMD$. The point $N$ is the intersection point between $AM$ and the parallel line to $CM$ that contains $B$. Prove that the triangle $BMN$ is equilateral if and only if $ABCD$ is a square.

Valentin Vornicu
3 replies
parmenides51
Sep 16, 2024
Tsikaloudakis
2 hours ago
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D1015 : A strange EF for polynomials
Dattier   1
N 2 hours ago by Dattier
Source: les dattes à Dattier
Find all $P \in \mathbb R[x,y]$ with $P \not\in \mathbb R[x] \cup \mathbb R[y]$ and $\forall g,f$ homeomorphismes of $\mathbb R$, $P(f,g)$ is an homoemorphisme too.
1 reply
Dattier
Mar 16, 2025
Dattier
2 hours ago
J
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Cutting a big square into smaller squares
nAalniaOMliO   4
N 2 hours ago by anudeep
Source: Belarusian National Olympiad 2020
A $20 \times 20$ checkered board is cut into several squares with integer side length. The size of a square is it's side length.
What is the maximum amount of different sizes this squares can have?
4 replies
nAalniaOMliO
Jan 29, 2025
anudeep
2 hours ago
J
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Proof Question
MathRook7817   3
N 5 hours ago by Jack_w
Prove or disprove the assertion that when $1/n$ is written in decimal form with n being a natural number, that it's decimal either terminates or is eventually periodic.

I saw this question somewhere and I thinks it's interesting.
3 replies
1 viewing
MathRook7817
Today at 2:19 AM
Jack_w
5 hours ago
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College Math Competitions
gavinhaominwang   6
N 6 hours ago by xHypotenuse
What are the major competitions that take place at college? For example HMMT.
6 replies
gavinhaominwang
Today at 1:39 AM
xHypotenuse
6 hours ago
J
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Trapezoid ABCD
tenniskidperson3   51
N Today at 5:15 AM by Curious_Droid
Source: 2009 USAMO problem 5
Trapezoid $ ABCD$, with $ \overline{AB}||\overline{CD}$, is inscribed in circle $ \omega$ and point $ G$ lies inside triangle $ BCD$. Rays $ AG$ and $ BG$ meet $ \omega$ again at points $ P$ and $ Q$, respectively. Let the line through $ G$ parallel to $ \overline{AB}$ intersects $ \overline{BD}$ and $ \overline{BC}$ at points $ R$ and $ S$, respectively. Prove that quadrilateral $ PQRS$ is cyclic if and only if $ \overline{BG}$ bisects $ \angle CBD$.
51 replies
tenniskidperson3
Apr 30, 2009
Curious_Droid
Today at 5:15 AM
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J
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hcssim application question
enya_yurself   3
N Yesterday at 7:30 PM by dppvlit123
do they send the Interesting Test to everyone who applied or do they read the friendly letter first and only send to the kids they like?
3 replies
enya_yurself
Monday at 11:13 PM
dppvlit123
Yesterday at 7:30 PM
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hcssim application question
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Reveal topic tags
HCSSiM
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enya_yurself
69 posts
enya_yurself
#1 h  Monday at 11:13 PM
Y by
do they send the Interesting Test to everyone who applied or do they read the friendly letter first and only send to the kids they like?
Z K Y
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lpieleanu
2807 posts
lpieleanu
#2 h  Monday at 11:23 PM
Y by
In the automated email following a submission of the preliminary form, it states that the Interesting Test will be sent on March 17, so it is sent to everyone.
Z K Y
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Magnetoninja
270 posts
Magnetoninja
#3 h  Yesterday at 1:35 AM
Y by
I believe they send to kids they like, I could be wrong tho
Z K Y
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dppvlit123
15 posts
dppvlit123
#4 h  Yesterday at 7:30 PM
Y by
Probably not, they emailed me 4 minutes after I sent mine in
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