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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 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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FE solution too simple?
Yiyj1   6
N 29 minutes ago by Primeniyazidayi
Source: 101 Algebra Problems from the AMSP
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that the equality $$f(f(x)+y) = f(x^2-y)+4f(x)y$$holds for all pairs of real numbers $(x,y)$.

My solution

I feel like my solution is too simple. Is there something I did wrong or something I missed?
6 replies
Yiyj1
Apr 9, 2025
Primeniyazidayi
29 minutes ago
J
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Combo problem
soryn   1
N an hour ago by soryn
The school A has m1 boys and m2 girls, and ,the school B has n1 boys and n2 girls. Each school is represented by one team formed by p students,boys and girls. If f(k) is the number of cases for which,the twice schools has,togheter k girls, fund f(k) and the valute of k, for which f(k) is maximum.
1 reply
soryn
5 hours ago
soryn
an hour ago
J
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Predicted AMC 8 Scores
megahertz13   167
N an hour ago by KF329
$\begin{tabular}{c|c|c|c}Username & Grade & AMC8 Score \\ \hline megahertz13 & 5 & 23 \\ \end{tabular}$
167 replies
megahertz13
Jan 25, 2024
KF329
an hour ago
J
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Two very hard parallel
jayme   5
N an hour ago by jayme
Source: own inspired by EGMO
Dear Mathlinkers,

1. ABC a triangle
2. D, E two point on the segment BC so that BD = DE= EC
3. M, N the midpoint of ED, AE
4. H the orthocenter of the acutangle triangle ADE
5. 1, 2 the circumcircle of the triangle DHM, EHN
6. P, Q the second point of intersection of 1 and BM, 2 and CN
7. U, V the second points of intersection of 2 and MN, PQ.

Prove : UV is parallel to PM.

Sincerely
Jean-Louis
5 replies
jayme
Yesterday at 12:46 PM
jayme
an hour ago
J
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Number theory
XAN4   1
N an hour ago by NTstrucker
Source: own
Prove that there exists infinitely many positive integers $x,y,z$ such that $x,y,z\ne1$ and $x^x\cdot y^y=z^z$.
1 reply
XAN4
Apr 20, 2025
NTstrucker
an hour ago
J
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R+ FE with arbitrary constant
CyclicISLscelesTrapezoid   25
N 2 hours ago by DeathIsAwe
Source: APMO 2023/4
Let $c>0$ be a given positive real and $\mathbb{R}_{>0}$ be the set of all positive reals. Find all functions $f \colon \mathbb{R}_{>0} \to \mathbb{R}_{>0}$ such that \[f((c+1)x+f(y))=f(x+2y)+2cx \quad \textrm{for all } x,y \in \mathbb{R}_{>0}.\]
25 replies
1 viewing
CyclicISLscelesTrapezoid
Jul 5, 2023
DeathIsAwe
2 hours ago
J
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Combo with cyclic sums
oVlad   1
N 3 hours ago by ja.
Source: Romania EGMO TST 2017 Day 1 P4
In $p{}$ of the vertices of the regular polygon $A_0A_1\ldots A_{2016}$ we write the number $1{}$ and in the remaining ones we write the number $-1.{}$ Let $x_i{}$ be the number written on the vertex $A_i{}.$ A vertex is good if \[x_i+x_{i+1}+\cdots+x_j>0\quad\text{and}\quad x_i+x_{i-1}+\cdots+x_k>0,\]for any integers $j{}$ and $k{}$ such that $k\leqslant i\leqslant j.$ Note that the indices are taken modulo $2017.$ Determine the greatest possible value of $p{}$ such that, regardless of numbering, there always exists a good vertex.
1 reply
oVlad
Yesterday at 1:41 PM
ja.
3 hours ago
J
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Stronger inequality than an old result
KhuongTrang   20
N 3 hours ago by KhuongTrang
Source: own, inspired
Problem. Find the best constant $k$ satisfying $$(ab+bc+ca)\left[\frac{1}{(a+b)^{2}}+\frac{1}{(b+c)^{2}}+\frac{1}{(c+a)^{2}}\right]\ge \frac{9}{4}+k\cdot\frac{a(a-b)(a-c)+b(b-a)(b-c)+c(c-a)(c-b)}{(a+b+c)^{3}}$$holds for all $a,b,c\ge 0: ab+bc+ca>0.$
20 replies
KhuongTrang
Aug 1, 2024
KhuongTrang
3 hours ago
J
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Incircle of a triangle is tangent to (ABC)
amar_04   11
N 3 hours ago by Nari_Tom
Source: XVII Sharygin Correspondence Round P18
Let $ABC$ be a scalene triangle, $AM$ be the median through $A$, and $\omega$ be the incircle. Let $\omega$ touch $BC$ at point $T$ and segment $AT$ meet $\omega$ for the second time at point $S$. Let $\delta$ be the triangle formed by lines $AM$ and $BC$ and the tangent to $\omega$ at $S$. Prove that the incircle of triangle $\delta$ is tangent to the circumcircle of triangle $ABC$.
11 replies
amar_04
Mar 2, 2021
Nari_Tom
3 hours ago
J
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Inspired by hlminh
sqing   1
N 3 hours ago by sqing
Source: Own
Let $ a,b,c $ be real numbers such that $ a^2+b^2+c^2=1. $ Prove that$$ |a-kb|+|kb-c|+|c-a|\leq 2\sqrt {k^2+1}$$Where $ k\geq 1.$
$$ |a-kb|+|kb-c|+|c-a|\leq 2\sqrt {2}$$Where $0< k\leq 1.$
1 reply
sqing
4 hours ago
sqing
3 hours ago
J
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Inequality with n-gon sides
mihaig   3
N 3 hours ago by mihaig
Source: VL
If $a_1,a_2,\ldots, a_n~(n\geq3)$ are are the lengths of the sides of a $n-$gon such that
$$\sum_{i=1}^{n}{a_i}=1,$$then
$$(n-2)\left[\sum_{i=1}^{n}{\frac{a_i^2}{(1-a_i)^2}}-\frac n{(n-1)^2}\right]\geq(2n-1)\left(\sum_{i=1}^{n}{\frac{a_i}{1-a_i}}-\frac n{n-1}\right)^2.$$
When do we have equality?

(V. Cîrtoaje and L. Giugiuc, 2021)
3 replies
mihaig
Feb 25, 2022
mihaig
3 hours ago
J
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Discuss the Stanford Math Tournament Here
Aaronjudgeisgoat   290
N 6 hours ago by techb
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag

Answers for the Algebra Subject Test
Estimated Algebra Cutoffs
Answers for the Geometry Subject Test
Estimated Geo Cutoffs
Answers for the Discrete Subject Test
Estimated Cutoffs for Discrete
Answers for the Team Round
Guts Answers
290 replies
Aaronjudgeisgoat
Apr 14, 2025
techb
6 hours ago
J
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MOP Emails
hellohannah   97
N 6 hours ago by Pengu14
So mop emails are probably coming tomorrow, feel free to discuss here. I'll probably post when I hear that they're out unless I'm asleep
97 replies
hellohannah
Yesterday at 4:59 AM
Pengu14
6 hours ago
J
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Tennessee Math Tournament (TMT) Online 2025
TennesseeMathTournament   77
N Today at 4:34 AM by Ruegerbyrd
Hello everyone! We are excited to announce a new competition, the Tennessee Math Tournament, created by the Tennessee Math Coalition! Anyone can participate in the virtual competition for free.

The testing window is from March 22nd to April 12th, 2025. Virtual competitors may participate in the competition at any time during that window.

The virtual competition consists of three rounds: Individual, Bullet, and Team. The Individual Round is 60 minutes long and consists of 30 questions (AMC 10 level). The Bullet Round is 20 minutes long and consists of 80 questions (Mathcounts Chapter level). The Team Round is 30 minutes long and consists of 16 questions (AMC 12 level). Virtual competitors may compete in teams of four, or choose to not participate in the team round.

To register and see more information, click here!

If you have any questions, please email connect@tnmathcoalition.org or reply to this thread!

Thank you to our lead sponsor, Jane Street!

IMAGE
77 replies
TennesseeMathTournament
Mar 9, 2025
Ruegerbyrd
Today at 4:34 AM
J
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J
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AMC and AIME help
jack_ma   9
N Apr 16, 2025 by bebebe
This year, I got a 3 on the AIME. I want to make olympiad by 2026. I made AIME by a small margin. To make olympiad, I need good scores on the AMC and AIME. What should I do to increase my AMC and AIME score?
9 replies
jack_ma
Apr 16, 2025
bebebe
Apr 16, 2025
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AMC and AIME help
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jack_ma
8 posts
jack_ma
#1 h  Apr 16, 2025, 12:33 AM
Y by
This year, I got a 3 on the AIME. I want to make olympiad by 2026. I made AIME by a small margin. To make olympiad, I need good scores on the AMC and AIME. What should I do to increase my AMC and AIME score?
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RollingPanda4616
222 posts
RollingPanda4616
#2 h  Apr 16, 2025, 12:36 AM • 1 Y
Y by jack_ma
Do alcumus and aops books, and mock past problem sets can get you a good start. :)
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jack_ma
8 posts
jack_ma
#3 h  Apr 16, 2025, 12:47 AM
Y by
How do I start learning about proves? Is there a class I can take besides woot?
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RollingPanda4616
222 posts
RollingPanda4616
#4 h  Apr 16, 2025, 12:49 AM • 1 Y
Y by jack_ma
Proofs are not needed on the AMC or AIME. :)
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jack_ma
8 posts
jack_ma
#5 h  Apr 16, 2025, 12:59 AM
Y by
I'm aware.
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Jaxman8
113 posts
Jaxman8
#6 h  Apr 16, 2025, 1:35 AM • 1 Y
Y by jack_ma
RollingPanda4616 wrote:
Do alcumus and aops books, and mock past problem sets can get you a good start. :)

Alcumus is good, but it isn’t that difficult. Is there like a different alcumus with harder problems besides math dash or amc trainer?
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programjames1
3046 posts
programjames1
#7 h  Apr 16, 2025, 1:56 AM • 1 Y
Y by jack_ma
jack_ma wrote:
How do I start learning about proofs? Is there a class I can take besides woot?

I think the easiest way to start proofs is to write up solutions on the AoPS forums. Solutions look very close to proofs, as long as you're not doing "fake solves" like Engineer's Induction. When you start on actual proof questions, start with easier olympiads or state competitions. For example, the Canadian Math Olympiad or the UNM-PNM. Questions on the High School Olympiads forum will usually be too difficult when you're just starting out, and besides it has a huge overrepresentation of geometry and inequalities.
This post has been edited 1 time. Last edited by programjames1, Apr 16, 2025, 1:56 AM
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RollingPanda4616
222 posts
RollingPanda4616
#8 h  Apr 16, 2025, 2:30 AM • 2 Y
Y by Jaxman8, jack_ma
Jaxman8 wrote:
RollingPanda4616 wrote:
Do alcumus and aops books, and mock past problem sets can get you a good start. :)

Alcumus is good, but it isn’t that difficult. Is there like a different alcumus with harder problems besides math dash or amc trainer?

I'm not aware of any alternatives. And also, Alcumus can get pretty hard. Turn the difficulty up to Insanely Hard, and do areas that you're weak in. :)
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akliu
1795 posts
akliu
#9 h  Apr 16, 2025, 2:39 AM • 2 Y
Y by jack_ma, RollingPanda4616
I recommend doing OTIS. I personally started doing this after I was trying to improve my AIME score, and had zero proof-writing experience whatsoever. You'll get the hang of it pretty soon, and it'll be really fun! By doing harder problems, you also train yourself to do easier problems.

For mock scores, I'd recommend just finding some AoPSwiki mocks for the AMCs, and doing past years' mocks for the AIME.
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bebebe
992 posts
bebebe
#10 h  Apr 16, 2025, 2:53 AM • 1 Y
Y by jack_ma
If you are having trouble with the concepts/big ideas, take classes on topics u haven't leanred on aops. Otherwise, it's a speed/problem solving issue, and then it's just about grinding.
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