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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
J
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New point on the circle
sman96   6
N a few seconds ago by ehuseyinyigit
Source: BdMO 2025 Secondary P3, Higher Secondary P2
Let $ABC$ be a given triangle with circumcenter $O$ and orthocenter $H$. Let $D, E$ and $F$ be the feet of the perpendiculars from $A, B$ and $C$ to the opposite sides, respectively. Let $A'$ be the reflection of $A$ with respect to $EF$. Prove that $HOA'D$ is a cyclic quadrilateral.

Proposed by Imad Uddin Ahmad Hasin
6 replies
sman96
Feb 8, 2025
ehuseyinyigit
a few seconds ago
J
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Olympiad question
slimshady360   2
N 4 minutes ago by SunnyEvan
Let a,b,c be positive real numbers such that a + b+c = 3abc. Prove that
a2 +b2 +c2 +3 ≥2(ab+bc+ca)
2 replies
slimshady360
2 hours ago
SunnyEvan
4 minutes ago
J
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hard number theory
blug   0
8 minutes ago
Find all primes $p$ such that $p^p+2$ is also prime.
0 replies
blug
8 minutes ago
0 replies
J
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help!!!!!!!!!!!!
Cobedangiu   0
9 minutes ago
help
0 replies
Cobedangiu
9 minutes ago
0 replies
J
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Euler totient and functional equation
AlperenINAN   4
N 15 minutes ago by ravengsd
Source: 2024 Turkey EGMO TST P2
Find all functions $f:\mathbb{Z}^{+} \rightarrow \mathbb{Z}^{+}$ such that the conditions

$\quad a) \quad a-b \mid f(a)-f(b)$ for all $a\neq b$ and $a,b \in \mathbb{Z}^{+}$

$\quad b) \quad f(\varphi(a))=\varphi(f(a))$ for all $a \in \mathbb{Z}^{+}$ where $\varphi$ is the Euler's totient function.

holds
4 replies
AlperenINAN
Feb 12, 2024
ravengsd
15 minutes ago
J
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Solve this
slimshady360   1
N 16 minutes ago by pooh123
Math problem
1 reply
slimshady360
2 hours ago
pooh123
16 minutes ago
J
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(a,b)-cuts for circles
navi_09220114   1
N 17 minutes ago by ja.
Source: Malaysian IMO TST 2025 P10
Let $m$ and $n$ be positive integers. Find all pairs of non-negative integers $a$ and $b$ that always satisfy the following condition:

Given any configuration of $m$ white dots and $n$ black dots on a circle, there always exist a line cutting the circle into two arcs, one of which consists of exactly $a$ white dots and $b$ black dots.

Proposed by Tan Min Heng
1 reply
navi_09220114
Yesterday at 1:08 PM
ja.
17 minutes ago
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Stronger than IMO 1988 P6
Entrepreneur   3
N an hour ago by Eagle116
Source: MONT
Show that if $ab+1$ divides $a^2+b^2$ for positive integers $a\;\&\;b,$ then
$$\textcolor{blue}{\frac{a^2+b^2}{ab+1}=\gcd(a,b)^2.}$$
3 replies
Entrepreneur
Jun 6, 2024
Eagle116
an hour ago
J
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A lot of tangent circle
ItzsleepyXD   3
N an hour ago by Kaimiaku
Source: Own
Let \( \triangle ABC \) be a triangle with circumcircle \( \omega \) and circumcenter \( O \). Let \( \omega_A \) and \( I_A \) represent the \( A \)-excircle and \( A \)-excenter, respectively. Denote by \( \omega_B \) the circle tangent to \( AB \), \( BC \), and \( \omega \) on the arc \( BC \) not containing \( A \), and similarly for \( \omega_C \). Let the tangency points of \( \omega_A, \omega_B, \omega_C \) with line \( BC \) be \( X, Y, Z \), respectively. Let \( P \neq A \) be the intersection point of \( (AYZ) \) and \( \omega \). Define \( Q \) as the point on segment \( OI_A \) such that \( 2 \cdot OQ = QI_A \). Suppose that \( XP \) intersects \( \omega \) again at \( R \). Let \( T \) be the touch point of the \( A \)-mixtilinear incircle and \( \omega \), and let \( A' \) be the antipode of \( A \) with respect to \( \omega \). Let \( S \) be the intersection of \( A'Q \) and \( I_AT \).

Show that the line \( RS \) is the radical axis of \( \omega_B \) and \( \omega_C \).
3 replies
ItzsleepyXD
5 hours ago
Kaimiaku
an hour ago
J
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Large root for quadratic polynomial
oVlad   4
N an hour ago by NicoN9
Source: 44th International Tournament of Towns, Senior A-Level P1, Fall 2022
What is the largest possible rational root of the equation $ax^2 + bx + c = 0{}$ where $a, b$ and $c{}$ are positive integers that do not exceed $100{}$?
4 replies
oVlad
Feb 16, 2023
NicoN9
an hour ago
J
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Sum of digits
srnjbr   0
an hour ago
Show that there exists a number b such that for every n>b, the sum of the digits of n! is at least 10^1000.
0 replies
srnjbr
an hour ago
0 replies
J
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Integer FE
GreekIdiot   3
N 2 hours ago by pco
Let $\mathbb{N}$ denote the set of positive integers
Find all $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all $a,b \in \mathbb{N}$ it holds that $f(ab+f(b+1))|bf(a+b)f(3b-2+a)$
3 replies
GreekIdiot
Yesterday at 8:53 PM
pco
2 hours ago
J
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Mathematics
slimshady360   1
N 2 hours ago by GreekIdiot
In a chess tournament with n ≥ 5 players, each player played all other players. One gets a point for a
win, half a point for a draw, and zero points for a loss. At the end of the tournament, each player had
a different number of points. Prove that the second and third ranked players had together more points
than the winner of the tournament.
1 reply
slimshady360
2 hours ago
GreekIdiot
2 hours ago
J
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Math Olympiad Workshops
kokcio   1
N 2 hours ago by GreekIdiot
Hello Math Enthusiasts!

I'm excited to announce a series of free Math Olympiad Workshops designed to help you sharpen your problem-solving skills in preparation for competitions. Whether you're a beginner or a seasoned competitor, these workshops aim to provide a supportive, challenging, and collaborative environment to explore advanced math topics.

Workshop Overview

Duration: 6 months (with the possibility of extending based on participant interest)

Structure: Weekly cycles, each dedicated to one of the main areas of Math Olympiad:
Week 1: Number Theory
Week 2: Geometry
Week 3: Algebra
Week 4: Combinatorics

Weekly Format
Monday: Problem Set Release: Approximately 30 problems will be posted covering the week's topic, which you will have chance to discuss.
Throughout the Week:
Theory Notes: I will share helpful theory and insights relevant to the problem set, giving you the tools you need to approach the problems.
Submission Opportunity: You can work on the problems and submit your solutions. I’ll review your work and provide feedback.
End of the Week: Solutions Post: I’ll release detailed solutions to all problems from the problem set.
Leaderboard: For those interested, we can maintain a table tracking participants who solve the most problems during the week.

Cycle Finale – Mock Contest
At the end of each 4-week cycle, we’ll host a Mock Contest featuring 4 problems (one from each topic). This is a great chance to simulate the competition environment and test your skills in a timed setting. I will review and provide feedback on your contest submissions.

Starting date: June 2

How to participate? Just write /signup under this post.

I believe these workshops will provide a comprehensive, engaging, and collaborative way to tackle Math Olympiad problems. I'm looking forward to seeing your creativity and problem-solving prowess!
If you have any questions or suggestions, please leave a comment below.
1 reply
kokcio
Today at 12:11 AM
GreekIdiot
2 hours ago
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J
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Interesting inequality
sqing   5
N Friday at 2:54 PM by sqing
Source: Own
Let $ a,b >0. $ Prove that
$$ \frac{1}{\frac{a}{a+b}+\frac{a}{2b}} +\frac{1}{\frac{b}{a+b}+\frac{1}{2}} +\frac{a}{2b} \geq \frac{5}{2} $$
5 replies
sqing
Feb 26, 2025
sqing
Friday at 2:54 PM
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Interesting inequality
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Reveal topic tags
inequalities proposed
inequalities
algebra
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Source: Own
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sqing
41181 posts
sqing
#1 h  Feb 26, 2025, 9:30 AM
Y by
Let $ a,b >0. $ Prove that
$$ \frac{1}{\frac{a}{a+b}+\frac{a}{2b}} +\frac{1}{\frac{b}{a+b}+\frac{1}{2}} +\frac{a}{2b} \geq \frac{5}{2} $$
Z K Y
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RagvaloD
4875 posts
RagvaloD
#2 h  Feb 26, 2025, 10:26 AM
Y by
Let $\frac{a}{b}=k$ then

$\frac{1}{\frac{a}{a+b}+\frac{a}{2b}} +\frac{1}{\frac{b}{a+b}+\frac{1}{2}} +\frac{a}{2b} =\frac{1}{\frac{k}{k+1}+\frac{k}{2}} +\frac{1}{\frac{1}{k+1}+\frac{1}{2}} +\frac{k}{2}=\frac{k+1}{k} *\frac{2(k+1)}{k+3}+\frac{k}{2}=\frac{(k-1)^2(k+4)}{2k(k+3)}+\frac{5}{2}\geq \frac{5}{2}$
Z K Y
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SunnyEvan
31 posts
SunnyEvan
#3 h  Feb 26, 2025, 10:33 AM
Y by
1/{ [a/(a+b)] + a/2b } + 1/{ [b/(a+b)] + b/2b) } + a/2b = [(1/a) + (1/b)]*{ [1/(a+b)] + 1/2b } + a/2b
use C-S : [(1/a) + (1/b)]*{ [1/(a+b)] + 1/2b } + a/2b ≥ 4/[(a/2b)+1.5] + a/2b
use AM-GM : 4/[(a/2b)+1.5] + a/2b ≥ 4 -1.5 = 2.5
This post has been edited 2 times. Last edited by SunnyEvan, Feb 26, 2025, 10:38 AM
Z K Y
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sqing
41181 posts
sqing
#4 h  Feb 26, 2025, 11:32 AM
Y by
Very nice.Thank RagvaloD.
Z K Y
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sqing
41181 posts
sqing
#5 h  Feb 26, 2025, 11:40 AM
Y by
Thanks.
Z K Y
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sqing
41181 posts
sqing
#7 h  Friday at 2:54 PM
Y by
$$\frac{1}{\frac{a}{a+b}+\frac{a}{2b}} +\frac{1}{\frac{b}{a+b}+\frac{b}{2b}} +\frac{a}{2b} = (\frac{1}{a} +\frac{1}{b})(\frac{1}{a+b} +\frac{1}{2b}) +\frac{a}{2b}$$$$\geq \frac{4}{\frac{a}{2b}+\frac{3}{2}} + \frac{a}{2b}=\frac{4}{\frac{a}{2b}+\frac{3}{2}} + \left(\frac{a}{2b}+\frac{3}{2}\right)-\frac{3}{2}\geq 4 -\frac{3}{2}= \frac{5}{2}$$Very very nice.
Thank SunnyEvan .
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