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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1571 replies
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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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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Gheorghe Țițeica 2025 Grade 11 P1
AndreiVila   1
N an hour ago by Mathzeus1024
Source: Gheorghe Țițeica 2025
Find all continuous functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $f(x+y)=f(x+f(y))$ for all $x,y\in\mathbb{R}$.
1 reply
AndreiVila
Yesterday at 9:40 PM
Mathzeus1024
an hour ago
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An Integral Inequality from the Chinese Internet
Blast_S1   1
N an hour ago by MS_asdfgzxcvb
Source: Xiaohongshu
Let $f(x)\in C[0,3]$ satisfy $f(x) \ge 0$ for all $x$ and
$$\int_0^3 \frac{1}{1 + f(x)}\,dx = 1.$$Show that
$$\int_0^3\frac{f(x)}{2 + f(x)^2}\,dx \le 1.$$
1 reply
Blast_S1
Today at 2:39 AM
MS_asdfgzxcvb
an hour ago
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CDF of normal distribution
We2592   1
N an hour ago by Tricky123
Q) We know that the PDF of normal distribution of $X$ id defined by
\[ f(x) = \frac{1}{\sqrt{2\pi} \sigma} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]now what is CDF or cumulative distribution function $F_X(x)=P[X\leq x]$

how to integrate ${-\infty} \to x$
please help
1 reply
We2592
Today at 2:09 AM
Tricky123
an hour ago
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Is this true?
Entrepreneur   1
N 2 hours ago by GreenKeeper
Source: Conjectured by me
$$\color{blue}{\frac ba\cdot\frac{a+1}{b+1}\cdot\frac{b+2}{a+2}\cdot\frac{a+3}{b+3}\cdots=\frac{\Gamma(\frac a2)\Gamma(\frac{b+1}{2})}{\Gamma(\frac b2)\Gamma(\frac{a+1}{2})}.}$$
1 reply
Entrepreneur
6 hours ago
GreenKeeper
2 hours ago
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something like MVT
mqoi_KOLA   0
3 hours ago
If $F$ is a continuous function on $[0,1]$ such that $F(0) = F(1)$, then there exists a $c \in (0,1)$ such that:

\[ F(c) = \frac{1}{c} \int_0^c F(x) \,dx \]
0 replies
mqoi_KOLA
3 hours ago
0 replies
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IGGM - Why Monopoly Go Is So Popular Among Video Games In 2025?
buyPOE2Currency   0
6 hours ago

What games do you think of when you mention board games? Perhaps Monopoly Go. After the game was launched on April 11, 2023, it was loved by many gamers and developed better and better in 2024. Why can Monopoly Go stand out among many similar games till today?

At the beginning of contact with a game, players often pay attention to the artistry of the game first. I believe that everyone has played some classic board games, and their painting styles are usually realistic or gorgeous. But Monopoly Go is very different at this time. Imagine a Monopoly Man who looks like a clay man leading you through the game world. Isn’t it interesting? The scenes and props in the game are as cute as jelly, which makes people want to continue playing.

In addition, Monopoly Go breaks through the limitations of traditional Monopoly games in terms of gameplay and incorporates card games, which makes players who like to collect excited. The game official will launch the Golden Lightning event from August 7, 2024, issuing new gold cards, which makes players love and hate. How can Monopoly Go Dice collected only through daily activities satisfy their needs for decorations and stickers in the game? I think maybe buying Monopoly Go Stickers on IGGM.com can help you.

Monopoly Go Stickers have distinguishes star ratings, which prompts players to constantly look for ways to get high-star stickers, especially every time the gold stickers are updated, the shiny colors and limited time limit make many players flock to it. I have to say that the game officials understand the mentality of our players very well.

In the new year, I believe that more players will join the game Monopoly Go, and more new activities can continue to bring better experience to players.
0 replies
buyPOE2Currency
6 hours ago
0 replies
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POECurrency - What Surprises Will PoE 2 Patch 0.2.0 Bring Us?
buyPOE2Currency   0
6 hours ago
The trailer for PoE 2 Patch 0.2.0 has been released. The female character running in the forest with a spear has aroused many players' expectations for this update. The official release date is not far away. Perhaps players can get a glimpse of more from the known information.

This update is named Dawn of the Hunt, which is undoubtedly closely related to the launch of Huntress. The official release date is set on April 4th. Some players may be familiar with this date because it is two days after the release of Last Epoch Season 2. Developer has caused dissatisfaction among some players because they are destined to make a choice between the two games, but there are still other players who think that they don't have to succumb to the minority.

Before the release on April 4th, developer will continue to release videos and texts to promote the upcoming live broadcast on March 27th. I believe that old PoE players are already used to this move. They always announce the less important changes first to arouse the curiosity of players, and announce the most important content in real time during the live broadcast. At that time, game directors Jonathan Rogers and Mark Roberts will also answer some questions of players in the community.

PoE 2 officials will release the complete patch notes after the live broadcast. The one week between the release of this information and the official release is a good time to grasp all the information, but now players should also have a certain understanding of the content.

The protagonist in the trailer of dozens of seconds is the new class, Huntress. This is a female character who is very close to Ranger in the passive skill tree. Her spear can attack from a distance and release huge damage in close combat. Such a novel attack method must have a lot of appeal in the game, so players who want to choose and build can master more information in advance.

Secondly, many new Support Gems will be released together. Currently, there are seven known items: Perfection, Battershout, Derange, Embitter, Concoct, Commiserate, and Volcanic Eruption. They have mixed reviews among players, but this may be due to differences in preferences for different classes. In any case, they give players more choices to a certain extent.

Unique items are also an aspect that players pay close attention to. Among them, The Hammer of Faith and The Bringer of Rain have caused heated discussions in a small range. The Bringer of Rain is an item that allows a class to use a two-handed weapon with one hand. Although it has very high requirements for the attributes of the weapon, as long as you have enough PoE 2 currency, it will still be a very useful skill for you. The existence of The Hammer of Faith seems to be a way for players to choose Warrior for construction, because its ability is to provide more than 230% physical damage, but it is unknown whether players will be shaken by this.

There is still limited information about PoE 2 Patch 0.2.0, so many players have made predictions. It is said that there will be an economic reset this time. I think there must be many players who need to make up for the gap with some old players through purchases. Visiting POECurrency.com will definitely give you satisfactory results.

Maybe you haven't finished all the current game content? That doesn't affect your curiosity about Dawn of the Hunt, because it is destined to be a major change.
0 replies
buyPOE2Currency
6 hours ago
0 replies
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Gheorghe Țițeica 2025 Grade 12 P3
AndreiVila   1
N Today at 8:43 AM by alexheinis
Source: Gheorghe Țițeica 2025
Let $\mathcal{P}_n$ be the set of all real monic polynomial functions of degree $n$. Prove that for any $a<b$, $$\inf_{P\in\mathcal{P}_n}\int_a^b |P(x)|\, dx >0.$$
Cristi Săvescu
1 reply
1 viewing
AndreiVila
Yesterday at 10:04 PM
alexheinis
Today at 8:43 AM
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Strange limit
Snoop76   1
N Today at 8:25 AM by alexheinis
Find: $\lim_{n \to \infty} n\cdot\sum_{k=1}^n \frac 1 {k(n-k)!}$
1 reply
Snoop76
Today at 7:42 AM
alexheinis
Today at 8:25 AM
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IGGM - Is Diablo 4 Season 8 Really An Exciting Boss Challenge?
buyPOE2Currency   0
Today at 7:43 AM
On March 11, the game developer released the PTR of Diablo 4 Season 8. After a week of experience, players have different opinions on the content of the new season.

Diablo 4 Season 8: Belial's Return is speculated to be officially released at the end of Season 7, that is, on April 29. Judging from the theme alone, Belial will return to Sanctuary this time. As one of the Lesser Evils in Diablo, its return will definitely bring new excitement to the game.

At present, the most obvious feeling of players about Season 8 is the upgrade of the game difficulty, which means that players will have to invest more resources in the future, such as Diablo 4 gold or Diablo 4 items. The reason why the developer did this may be that it found that players always entered the Endgame too early in previous seasons. This is particularly evident in Season of Witchcraft. It only takes an amazing nine hours for players to reach level 60! In order to change the status quo, Diablo 4 has modified the probability of item drops, and players will say goodbye to the Legendary items that were easy to obtain in the past.

In the new season, the theme of the game will change from witch power to boss power. This is a new power system. Players will collect their power by defeating 24 bosses for their own use. Each power contains Main Power and a Modifier Power. Players can use a Main Power and use three Modifier Powers to strengthen it. This will have a lot of room and possibilities for the construction of classes, and will experience a very different way of attacking than before.

In addition, Season 8 has also reset the Endgame boss fights. Lair Bosses are divided into three levels: Initiate, Greater, and Exalted. After players break through various levels, they can fight the most difficult battle with Belial, the Lord of Lies in Exalted difficulty. Although the mechanism that players need to spend special materials to summon them has been changed this time, they need to spend the corresponding Lair Key to collect the spoils of defeating the boss. This seems to be a positive change, as players only need to spend when they succeed.

Compared with the previous Helltide and Headhunts, the Apparition Incursion event, the main way for players to gain Boss power, has also changed. The changes of Boss have increased in level. After entering the event at the location marked on the map, players need to defeat the Apparition monsters first, and then defeat the Apparition Boss that you have angered. At this time, if you are lucky enough to defeat two waves of enemies, Belial will attack you as the final Boss. If your ability or equipment is not enough to resist its heavy blow, then at this time, I highly recommend you to buy Diablo 4 items on IGGM.com like me. After all, improving your equipment is the basis for victory.

Although Diablo 4 Season 8 has undergone a reform in difficulty, it has not added any additional interesting mechanisms at present, which is also a point of dissatisfaction for many players. However, there is still some time before the official release, and the specific development is still worth looking forward to.

0 replies
buyPOE2Currency
Today at 7:43 AM
0 replies
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Romanian National Olympiad 1999 - Grade 12 - Problem 4
Filipjack   4
N Today at 7:26 AM by KevinYang2.71
Source: Romanian National Olympiad 1999 - Grade 12 - Problem 4
Let $A$ be an integral domain and $A[X]$ be its associated ring of polynomials. For every integer $n \ge 2$ we define the map $\varphi_n : A[X] \to A[X],$ $\varphi_n(f)=f^n$ and we assume that the set $$M= \Big\{ n \in \mathbb{Z}_{\ge 2} : \varphi_n \mathrm{~is~an~endomorphism~of~the~ring~} A[X] \Big\}$$is nonempty.

Prove that there exists a unique prime number $p$ such that $M=\{p,p^2,p^3, \ldots\}.$
4 replies
Filipjack
Jan 30, 2025
KevinYang2.71
Today at 7:26 AM
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The ratio between two integral
Butterfly   2
N Today at 5:58 AM by vanstraelen



Prove $\frac{I_1}{I_2}=\sqrt{2}$ where $I_1=\int_{0}^{\frac{\sqrt{3}-1}{\sqrt{2}}} \frac{1-x^2}{\sqrt{x^8-14x^4+1}}dx$ and $I_2=\int_{0}^{\sqrt{2}-1} \frac{1+x^2}{\sqrt{x^8+14x^4+1}}dx.$
2 replies
Butterfly
Yesterday at 1:23 AM
vanstraelen
Today at 5:58 AM
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Matrix in terms of exp
RenheMiResembleRice   0
Today at 3:05 AM
$\begin{pmatrix}X\left(t\right)\\ Y\left(t\right)\end{pmatrix}=\begin{pmatrix}\frac{1}{\sqrt{2}}&-\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}&\frac{1}{\sqrt{2}}\end{pmatrix}\begin{pmatrix}x\left(t\right)\\ y\left(t\right)\end{pmatrix}$

$X\left(t\right)=a_1e^t+a_2e^{-t}+a_3$
Find $a_1$, $a_2$, and $a_3$.
0 replies
RenheMiResembleRice
Today at 3:05 AM
0 replies
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Gheorghe Țițeica 2025 Grade 12 P1
AndreiVila   1
N Today at 1:22 AM by KAME06
Source: Gheorghe Țițeica 2025
Let $G$ be a finite group and $a\in G$ a fixed element. Define the set $$S_a=\{g\in G\mid ga\neq ag, \,ga^2=a^2g\}.$$Show that:
[list=a]
[*] if $g\in S_a$, then $ag^{-1}\in S_a$;
[*] $|S_a|$ is divisible by $4$.
1 reply
AndreiVila
Yesterday at 9:58 PM
KAME06
Today at 1:22 AM
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J
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Time Scale Calculus- Dynamical inequalities
ehuseyinyigit   3
N Today at 1:10 AM by paxtonw
Does Maclaurin's Inequality have a dynamic version in time scale calculus, especially for diamond alpha calculus?
3 replies
ehuseyinyigit
Mar 23, 2025
paxtonw
Today at 1:10 AM
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Time Scale Calculus- Dynamical inequalities
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ehuseyinyigit
790 posts
ehuseyinyigit
#1 h  Mar 23, 2025, 10:05 AM
Y by
Does Maclaurin's Inequality have a dynamic version in time scale calculus, especially for diamond alpha calculus?
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ehuseyinyigit
790 posts
ehuseyinyigit
#2 h  Mar 23, 2025, 11:20 AM
Y by
There exists dynamuc versions of Radon's, Jensen's and Nesbitt's Inequality, but I need MACLAURIN.
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ehuseyinyigit
790 posts
ehuseyinyigit
#3 h  Mar 26, 2025, 6:13 PM
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Anyone??
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paxtonw
5 posts
paxtonw
#4 h  Today at 1:10 AM
Y by
Doesn't exist
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