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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

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

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

Inminimumlity

giangtruong13 1

N 7 minutes ago by giangtruong13

Let $a,b,c>0$ and $\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \leq 3$ . Find the minimum: $A=\sum_{cyc} \frac{1}{\sqrt{a^2-ab+3b^2+1}}$

1 reply

+1 w

giangtruong13

3 hours ago

giangtruong13

7 minutes ago

Exquality

giangtruong13 2

N 8 minutes ago by lbh_qys

Let $x,y,z>0$ satisfy that: $(xz)^2+(yz)^2+1 \leq 3z$ . Find the minimum value: $P=\frac{1}{(x+1)^2}+\frac{8}{(y+3)^2}+\frac{4z^2}{(1+2z)^2}$

2 replies

giangtruong13

an hour ago

lbh_qys

8 minutes ago

Problem 2830

sqing 0

15 minutes ago

Source: SXTB (2)2025

Let $a,b>0$ and $\frac{1}{a^2+1}+ \frac{1}{b^2+1}=t$ $(1<t<2).$ Find the value range of $a+b.$
h

0 replies

1 viewing

sqing

15 minutes ago

0 replies

Set theory false statement

RenheMiResembleRice 5

N 25 minutes ago by LawofCosine

Prove or show the following statement does not hold
B−(A−B)=(A∪B)

5 replies

RenheMiResembleRice

an hour ago

LawofCosine

25 minutes ago

IMO PSC said it's not novel, but it's still very pretty

mshtand1 1

N 29 minutes ago by Rushery_10

Source: Ukrainian Mathematical Olympiad 2025. Day 1, Problem 10.3

It is known that some $d$ distinct divisors of a positive integer number $n$ form an arithmetic progression. Prove that the number $n$ has at least $2d - 2$ divisors.

Proposed by Anton Trygub

1 reply

mshtand1

Mar 13, 2025

Rushery_10

29 minutes ago

geometry party

pnf 1

N 41 minutes ago by Tsikaloudakis

https://artofproblemsolving.com/community/c4260013_geometry_party

1 reply

pnf

Yesterday at 1:51 PM

Tsikaloudakis

41 minutes ago

chat gpt

fuv870 31

N 43 minutes ago by Quantum-Phantom

The chat gpt alreadly knows how to solve the problem of IMO USAMO and AMC?

31 replies

fuv870

Yesterday at 9:51 PM

Quantum-Phantom

43 minutes ago

Find the value

sqing 3

N an hour ago by sqing

Source: Own

Let $a,b,c$ be distinct real numbers such that $\frac{a^2}{(a-b)^2}+ \frac{b^2}{(b-c)^2}+ \frac{c^2}{(c-a)^2} =1.$ Find the value of $\frac{a}{a-b}+ \frac{b}{b-c}+ \frac{c}{c-a}.$
Let $a,b,c$ be distinct real numbers such that $\frac{a^2}{(b-c)^2}+ \frac{b^2}{(c-a)^2}+ \frac{c^2}{(a-b)^2}=2.$ Find the value of $\frac{a}{b-c}+ \frac{b}{c-a}+ \frac{c}{a-b}.$
Let $a,b,c$ be distinct real numbers such that $\frac{(a+b)^2}{(a-b)^2}+ \frac{(b+c)^2}{(b-c)^2}+ \frac{(c+a)^2}{(c-a)^2}=2.$ Find the value of $\frac{a+b}{a-b}+\frac{b+c}{b-c}+ \frac{c+a}{c-a}.$

3 replies

sqing

3 hours ago

sqing

an hour ago

Kaprekar Number

CSJL 4

N an hour ago by Korean_fish_Kaohsiung

Source: 2025 Taiwan TST Round 1 Independent Study 2-N

Let $k$ be a positive integer. A positive integer $n$ is called a $k$ -good number if it satisfies
the following two conditions:

1. $n$ has exactly $2k$ digits in decimal representation (it cannot have leading zeros).

2. If the first $k$ digits and the last $k$ digits of $n$ are considered as two separate $k$ -digit
numbers (which may have leading zeros), the square of their sum is equal to $n$ .

For example, $2025$ is a $2$ -good number because
$(20 + 25)^2 = 2025.$ Find all $3$ -good numbers.

4 replies

CSJL

Mar 6, 2025

Korean_fish_Kaohsiung

an hour ago

Functional Inequality Implies Uniform Sign

peace09 30

N an hour ago by Nari_Tom

Source: 2023 ISL A2

Let $\mathbb{R}$ be the set of real numbers. Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f(x+y)f(x-y)\geqslant f(x)^2-f(y)^2$ for every $x,y\in\mathbb{R}$ . Assume that the inequality is strict for some $x_0,y_0\in\mathbb{R}$ .

Prove that either $f(x)\geqslant 0$ for every $x\in\mathbb{R}$ or $f(x)\leqslant 0$ for every $x\in\mathbb{R}$ .

30 replies

peace09

Jul 17, 2024

Nari_Tom

an hour ago

orthogonality

karimeow 0

2 hours ago

Given a cyclic quadrilateral ABCD inscribed in the circle (O). Let E and F be the intersections of AD with BC and AC with BD, respectively. Prove that the circle with diameter EF is orthogonal to (O).

0 replies

karimeow

2 hours ago

0 replies

Problem 4

teps 73

N 2 hours ago by Nari_Tom

Find all functions $f:\mathbb Z\rightarrow \mathbb Z$ such that, for all integers $a,b,c$ that satisfy $a+b+c=0$ , the following equality holds:
$f(a)^2+f(b)^2+f(c)^2=2f(a)f(b)+2f(b)f(c)+2f(c)f(a).$
(Here $\mathbb{Z}$ denotes the set of integers.)

Proposed by Liam Baker, South Africa

73 replies

teps

Jul 11, 2012

Nari_Tom

2 hours ago

Reflexive Polynomial

awesomeming327. 2

N 2 hours ago by GoldenFirefly92

Source: CMO 2025

A polynomial $c_dx^d+c_{d-1}x^{d-1}+\dots+c_1x+c_0$ with degree $d$ is reflexive if there is an integer $n\ge d$ such that $c_i=c_{n-i}$ for every $0\le i\le n$ , where $c_i=0$ for $i>d$ . Let $\ell\ge 2$ be an integer and $p(x)$ be a polynomial with integer coefficients. Prove that there exist reflexive polynomials $q(x)$ , $r(x)$ with integer coefficients such that
$(1+x+x^2+\dots+x^{\ell-1})p(x)=q(x)+x^\ell r(x)$

2 replies

awesomeming327.

Mar 7, 2025

GoldenFirefly92

2 hours ago

Problem 1 of Fourth round

Pinko 2

N 3 hours ago by Assassino9931

Source: V International Festival of Young Mathematicians Sozopol 2014, Theme for 10-12 grade

Find all pairs of natural numbers $(m,n)$ , for which $m\mid 2^{\varphi(n)} +1$ and $n\mid 2^{\varphi (m)} +1$ .

2 replies

Pinko

Oct 13, 2019

Assassino9931

3 hours ago

chat gpt

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Reveal topic tags

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2 posts

fuv870

#1 h Yesterday at 9:51 PM

Y by

The chat gpt alreadly knows how to solve the problem of IMO USAMO and AMC?

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225 posts

#2 h Yesterday at 9:58 PM

Y by

no it doesnt unless it was already a leaked problem on the internet. If you give it a IMO level question you made up, small chance it is going to get it right

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2 posts

fuv870

#3 h Yesterday at 10:03 PM

Y by

But I heard that ChatGPT-3.5 is better than 4.0 at solving math?

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ohiorizzler1434

713 posts

ohiorizzler1434

#4 h Today at 1:06 AM

Y by

Bro! Are you promoting the usage of ChatGPT in mathematical olympiads? It is well known that ChatGPT often fakesolves problems! Maybe you should work on your own mathematical skills than drawing attention away from legit mathematical causes with your promotion of AI in mathematical olympiads! Stop being unethical now!

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261 posts

#5 h Today at 1:08 AM

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chill bro

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968 posts

#6 h Today at 1:09 AM • 2 Y

Y by jkim0656, aidan0626

ohiorizzler1434 wrote:

Bro! Are you promoting the usage of ChatGPT in mathematical olympiads? It is well known that ChatGPT often fakesolves problems! Maybe you should work on your own mathematical skills than drawing attention away from legit mathematical causes with your promotion of AI in mathematical olympiads! Stop being unethical now!

ohiorizzler1434 wrote:

I think the rise of AI will help America. With AI, anyone can solve maths problems and create amazing art and music, thus preventing the classist issue of the higher classes learning mathematics and art and instruments from disadvantaging everyone else.

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261 posts

#7 h Today at 1:12 AM

Y by

scannose wrote:

ohiorizzler1434 wrote:

Bro! Are you promoting the usage of ChatGPT in mathematical olympiads? It is well known that ChatGPT often fakesolves problems! Maybe you should work on your own mathematical skills than drawing attention away from legit mathematical causes with your promotion of AI in mathematical olympiads! Stop being unethical now!

ohiorizzler1434 wrote:

I think the rise of AI will help America. With AI, anyone can solve maths problems and create amazing art and music, thus preventing the classist issue of the higher classes learning mathematics and art and instruments from disadvantaging everyone else.

Fr! lol

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ohiorizzler1434

713 posts

ohiorizzler1434

#8 h Today at 1:38 AM

Y by

By immediately attacking me for my opinions, you have revealed your ignorance of olympiad maths. While ChatGPT and other LLMs are clearly capable of solving simple linear or quadratic equations, and basic mathematical modeling problems are no problem for it, you are ignoring that this forum is under the name 'HIGH SCHOOL OLYMPIADS', not 'MIDDLE SCHOOL MATHS'. I'm just suggesting that AI can help many people without access to mathematical resources, a good way to learn and improve, which is in no way related to the elitist olympiad mathematics. In olympiad mathematics, AI has no purpose and should never be used.

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261 posts

#9 h 6 hours ago

Y by

ohiorizzler1434 wrote:

By immediately attacking me for my opinions, you have revealed your ignorance of olympiad maths. While ChatGPT and other LLMs are clearly capable of solving simple linear or quadratic equations, and basic mathematical modeling problems are no problem for it, you are ignoring that this forum is under the name 'HIGH SCHOOL OLYMPIADS', not 'MIDDLE SCHOOL MATHS'. I'm just suggesting that AI can help many people without access to mathematical resources, a good way to learn and improve, which is in no way related to the elitist olympiad mathematics. In olympiad mathematics, AI has no purpose and should never be used.

i disagree, i think limiting AI's potential to only lower level math will hinder its development anyhow.
Furthermore, just wait a few years until deepseek and gpts start acing amcs and amies

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ohiorizzler1434

713 posts

ohiorizzler1434

#10 h 4 hours ago

Y by

That is impossible! Imagine thinking that a language model is capable of solving mathematical problems involving complex thinking and creative methods. This is a preposterous statement that seeks to claim that AI can replace humans.

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223 posts

#11 h 4 hours ago

Y by

I think google's alphago or something like that solved 4 out of 6 IMO problems 4 2024

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ohiorizzler1434

713 posts

ohiorizzler1434

#12 h 4 hours ago

Y by

Alphageo is not ChatGPT. Alphageo mixes a specialised AI to make geometric claims with a logical proof software. Furthermore, do you really believe that Alphageo is good? Remember that Alphageo is sponsored by a massive website company called Google, which means that it will likely have biased testing results that only make Google look good. It is very likely that Google chooses several IMO problems and pretends to solve them under Alphageo.

Also, where are you getting your statistics from? How could alphaGEO solve 4 out of 6 problems when there was only 1 geometry problem? Please inform yourself of the real situation before commenting on this issue.

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261 posts

#13 h 4 hours ago

Y by

ohiorizzler1434 wrote:

That is impossible! Imagine thinking that a language model is capable of solving mathematical problems involving complex thinking and creative methods. This is a preposterous statement that seeks to claim that AI can replace humans.

just wait and see
AI is going to take the world by storm in at most a year by now...

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261 posts

#14 h 4 hours ago

Y by

i like how this thread has degenerated into a debate about AI capabilities

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223 posts

#15 h 4 hours ago • 1 Y

Y by jkim0656

@ohiorizzler1434 u really gotta chill.

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570 posts

#16 h 4 hours ago

Y by

fuv870 wrote:

The chat gpt alreadly knows how to solve the problem of IMO USAMO and AMC?

Yes in a way, but it codes them or bashes most out for AIME and AMC. For USAMO and IMO, it knows key ideas of solution, but only the very top AI's can solve some problems that level with 7/7 solutions. But soon enough, AI will be smart enough to do most IMO problems. Not yet though..

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ohiorizzler1434

713 posts

ohiorizzler1434

#17 h 4 hours ago

Y by

Your claims reflect a fundamental misunderstanding of the capabilities of AI. It's like saying, one day humans will be strong enough to fly without aid. ChatGPT is fundamentally incapable of solving IMO problems, just admit it.

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570 posts

#18 h 4 hours ago

Y by

ohiorizzler1434 wrote:

Your claims reflect a fundamental misunderstanding of the capabilities of AI. It's like saying, one day humans will be strong enough to fly without aid. ChatGPT is fundamentally incapable of solving IMO problems, just admit it.

Nah it is most definitely gonna be able to solve IMO problems in the future :skull: especially when more of us aops people go into the AI field when we get older.

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ohiorizzler1434

713 posts

ohiorizzler1434

#19 h 3 hours ago

Y by

Just because there are AoPSers working in AI does not mean they will make significant contributions to the development of AI, nor overcome the fundamental issues with ChatGPT.

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#20 h 3 hours ago

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Schintalpati wrote:

ohiorizzler1434 wrote:

Your claims reflect a fundamental misunderstanding of the capabilities of AI. It's like saying, one day humans will be strong enough to fly without aid. ChatGPT is fundamentally incapable of solving IMO problems, just admit it.

Nah it is most definitely gonna be able to solve IMO problems in the future :skull: especially when more of us aops people go into the AI field when we get older.

So true

i mean look at people who said that we would never get to the moon...
everything seems impossible until someone does it :play_ball:

:play_ball:

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ohiorizzler1434

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ohiorizzler1434

#21 h 3 hours ago

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I did not talk about landing on the moon. The technology and concept behind rockets were well known for a long period before the moon landings.

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#22 h 3 hours ago

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ohiorizzler1434 wrote:

I did not talk about landing on the moon. The technology and concept behind rockets were well known for a long period before the moon landings.

well the tech and concepts for AI is also well known now, even though it can't YET ace a IMO

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ohiorizzler1434

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ohiorizzler1434

#23 h 3 hours ago

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I was never talking about AI in general, only about how ChatGPT and other LLMs have a structure incapable of comprehending rigorous mathematics and solving hard problems like this.

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#24 h 3 hours ago

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ohiorizzler1434 wrote:

I was never talking about AI in general, only about how ChatGPT and other LLMs have a structure incapable of comprehending rigorous mathematics and solving hard problems like this.

i can't say i agree.
its true that LLMs cant do these things now, but the technological advancements of just AI over the past year is amazing, if u look at it from another perspective.
LLMs take in data and learn from it, like a human brain. They can analyze things from thousands of different perspectives and find one that works. It's hard to say that AI will NEVER be able to catch up to an IMO level participant, as a result.

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#25 h 3 hours ago

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we had a good debate, @ohiorizzler1434

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#26 h 3 hours ago

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AI is actually good at Math but it is often saying :"This problem cant be solved 'cuz it's wrong"

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ohiorizzler1434

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ohiorizzler1434

#27 h 2 hours ago

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jkim0656 wrote:

ohiorizzler1434 wrote:

I was never talking about AI in general, only about how ChatGPT and other LLMs have a structure incapable of comprehending rigorous mathematics and solving hard problems like this.

i can't say i agree.
its true that LLMs cant do these things now, but the technological advancements of just AI over the past year is amazing, if u look at it from another perspective.
LLMs take in data and learn from it, like a human brain. They can analyze things from thousands of different perspectives and find one that works. It's hard to say that AI will NEVER be able to catch up to an IMO level participant, as a result.

You are wrong. LLMs have an intrinsic capability to analyse language phrases so it is impossible for them to understand the rigorous first-order logic underlying mathematics, like set theory or geometry.

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Iveela

#28 h 2 hours ago

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fuv870 wrote:

The chat gpt alreadly knows how to solve the problem of IMO USAMO and AMC?

Please lock this post. Very disappointing.

This post has been edited 1 time. Last edited by Iveela, 2 hours ago

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ohiorizzler1434

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ohiorizzler1434

#29 h 2 hours ago

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I agree too. This discussion has led to nobody changing their opinions and improving their understanding of AIs.

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Quantum-Phantom

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Quantum-Phantom

#30 h 2 hours ago

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ohiorizzler1434 wrote:

You are wrong. LLMs have an intrinsic capability to analyse language phrases so it is impossible for them to understand the rigorous first-order logic underlying mathematics, like set theory or geometry.

Have you heard of mathematics formalized tools, such as "LEAN"?

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ohiorizzler1434

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ohiorizzler1434

#31 h 2 hours ago

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LEAN is completely different to LLMs. Please read the argument above and stop making irrelevant points.

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Quantum-Phantom

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Quantum-Phantom

#32 h 43 minutes ago

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Who gave you the confidence to make all these claims and refutes?

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