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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
k i Suggestion Form
jwelsh   0
May 6, 2021
Hello!

Given the number of suggestions we’ve been receiving, we’re transitioning to a suggestion form. If you have a suggestion for the AoPS website, please submit the Google Form:
Suggestion Form

To keep all new suggestions together, any new suggestion threads posted will be deleted.

Please remember that if you find a bug outside of FTW! (after refreshing to make sure it’s not a glitch), make sure you’re following the How to write a bug report instructions and using the proper format to report the bug.

Please check the FTW! thread for bugs and post any new ones in the For the Win! and Other Games Support Forum.
0 replies
jwelsh
May 6, 2021
0 replies
k i Read me first / How to write a bug report
slester   3
N May 4, 2019 by LauraZed
Greetings, AoPS users!

If you're reading this post, that means you've come across some kind of bug, error, or misbehavior, which nobody likes! To help us developers solve the problem as quickly as possible, we need enough information to understand what happened. Following these guidelines will help us squash those bugs more effectively.

Before submitting a bug report, please confirm the issue exists in other browsers or other computers if you have access to them.

For a list of many common questions and issues, please see our user created FAQ, Community FAQ, or For the Win! FAQ.

What is a bug?
A bug is a misbehavior that is reproducible. If a refresh makes it go away 100% of the time, then it isn't a bug, but rather a glitch. That's when your browser has some strange file cached, or for some reason doesn't render the page like it should. Please don't report glitches, since we generally cannot fix them. A glitch that happens more than a few times, though, could be an intermittent bug.

If something is wrong in the wiki, you can change it! The AoPS Wiki is user-editable, and it may be defaced from time to time. You can revert these changes yourself, but if you notice a particular user defacing the wiki, please let an admin know.

The subject
The subject line should explain as clearly as possible what went wrong.

Bad: Forum doesn't work
Good: Switching between threads quickly shows blank page.

The report
Use this format to report bugs. Be as specific as possible. If you don't know the answer exactly, give us as much information as you know. Attaching a screenshot is helpful if you can take one.

Summary of the problem:
Page URL:
Steps to reproduce:
1.
2.
3.
...
Expected behavior:
Frequency:
Operating system(s):
Browser(s), including version:
Additional information:


If your computer or tablet is school issued, please indicate this under Additional information.

Example
Summary of the problem: When I click back and forth between two threads in the site support section, the content of the threads no longer show up. (See attached screenshot.)
Page URL: http://artofproblemsolving.com/community/c10_site_support
Steps to reproduce:
1. Go to the Site Support forum.
2. Click on any thread.
3. Click quickly on a different thread.
Expected behavior: To see the second thread.
Frequency: Every time
Operating system: Mac OS X
Browser: Chrome and Firefox
Additional information: Only happens in the Site Support forum. My tablet is school issued, but I have the problem at both school and home.

How to take a screenshot
Mac OS X: If you type ⌘+Shift+4, you'll get a "crosshairs" that lets you take a custom screenshot size. Just click and drag to select the area you want to take a picture of. If you type ⌘+Shift+4+space, you can take a screenshot of a specific window. All screenshots will show up on your desktop.

Windows: Hit the Windows logo key+PrtScn, and a screenshot of your entire screen. Alternatively, you can hit Alt+PrtScn to take a screenshot of the currently selected window. All screenshots are saved to the Pictures → Screenshots folder.

Advanced
If you're a bit more comfortable with how browsers work, you can also show us what happens in the JavaScript console.

In Chrome, type CTRL+Shift+J (Windows, Linux) or ⌘+Option+J (Mac).
In Firefox, type CTRL+Shift+K (Windows, Linux) or ⌘+Option+K (Mac).
In Internet Explorer, it's the F12 key.
In Safari, first enable the Develop menu: Preferences → Advanced, click "Show Develop menu in menu bar." Then either go to Develop → Show Error console or type Option+⌘+C.

It'll look something like this:
IMAGE
3 replies
slester
Apr 9, 2015
LauraZed
May 4, 2019
k i Community Safety
dcouchman   0
Jan 18, 2018
If you find content on the AoPS Community that makes you concerned for a user's health or safety, please alert AoPS Administrators using the report button (Z) or by emailing sheriff@aops.com . You should provide a description of the content and a link in your message. If it's an emergency, call 911 or whatever the local emergency services are in your country.

Please also use those steps to alert us if bullying behavior is being directed at you or another user. Content that is "unlawful, harmful, threatening, abusive, harassing, tortuous, defamatory, vulgar, obscene, libelous, invasive of another's privacy, hateful, or racially, ethnically or otherwise objectionable" (AoPS Terms of Service 5.d) or that otherwise bullies people is not tolerated on AoPS, and accounts that post such content may be terminated or suspended.
0 replies
dcouchman
Jan 18, 2018
0 replies
PE is bisector of BPC
goldeneagle   44
N 7 minutes ago by cursed_tangent1434
Source: Iran TST 2012 -first day- problem 2
Consider $\omega$ is circumcircle of an acute triangle $ABC$. $D$ is midpoint of arc $BAC$ and $I$ is incenter of triangle $ABC$. Let $DI$ intersect $BC$ in $E$ and $\omega$ for second time in $F$. Let $P$ be a point on line $AF$ such that $PE$ is parallel to $AI$. Prove that $PE$ is bisector of angle $BPC$.

Proposed by Mr.Etesami
44 replies
1 viewing
goldeneagle
Apr 23, 2012
cursed_tangent1434
7 minutes ago
find question
mathematical-forest   9
N 12 minutes ago by JARP091
Are there any contest questions that seem simple but are actually difficult? :-D
9 replies
mathematical-forest
May 29, 2025
JARP091
12 minutes ago
Interesting inequality
sqing   1
N 24 minutes ago by Zok_G8D
Source: Own
Let $  a, b,c>0,b+c\geq 3a$. Prove that
$$ \sqrt{\frac{a}{b+c-a}}-\frac{ 2a^2-b^2-c^2}{(a+b)(a+c)}\geq \frac{2}{5}+\frac{1}{\sqrt 2}$$$$ \frac{3}{2}\sqrt{\frac{a}{b+c-a}}-\frac{ 2a^2-b^2-c^2}{(a+b)(a+c)}\geq \frac{2}{5}+\frac{3}{2\sqrt 2}$$
1 reply
sqing
Yesterday at 2:49 AM
Zok_G8D
24 minutes ago
Basic ideas in junior diophantine equations
Maths_VC   6
N 26 minutes ago by Adywastaken
Source: Serbia JBMO TST 2025, Problem 3
Determine all positive integers $a, b$ and $c$ such that
$2$ $\cdot$ $10^a + 5^b = 2025^c$
6 replies
Maths_VC
May 27, 2025
Adywastaken
26 minutes ago
k cannot make new forum
CuteBaby   10
N Sep 23, 2024 by bpan2021
i cant make new forum
10 replies
CuteBaby
Sep 21, 2024
bpan2021
Sep 23, 2024
Problems From The Book Forum
kingu   2
N Jun 12, 2024 by kingu
I already know that this is a common question, but how does one gain accesses to the PFTB forum's if possible? If it is not, then does this mean that I can create the relevant forum?
I'm thankful for any response.
2 replies
kingu
Jun 12, 2024
kingu
Jun 12, 2024
k Forum question
Kawhi2   3
N May 29, 2024 by KangarooPrecise
How does Aops rank user created forums? Like, do they rank it by posts, or threads?
3 replies
Kawhi2
May 29, 2024
KangarooPrecise
May 29, 2024
k Closing a Dialogue Box Causes Inability to Create Forum
bpan2021   2
N Dec 19, 2023 by jlacosta
Summary of the problem: When making a forum, you must set your forum to be public or private. When you click on the "CREATE" button, you are asked if your forum will be public or private. When you click on the "X" button on the dialogue, you are unable to create the forum anymore, because the "CREATE" button turns unresponsive.
Page URL: https://artofproblemsolving.com/community/category-admin/forum.
Steps to reproduce:
1. Click on the link.
2. Insert random information into the boxes. ...
3. Click the "CREATE" button.
4. Undo that action by pressing the upper "X" above the dialogue box. ...
5. Observe what happens when you try to create the forum afterward.
Expected behavior: The forum will proceed to create when the button is clicked.
Frequency: 6/6 = 100%.
Operating system(s): Windows 11, ChromeOS.
Browser(s), including version: Google Chrome 120.
Additional information: Refreshing allowed me to create a forum again, only if the steps three and four were not followed.
2 replies
bpan2021
Dec 18, 2023
jlacosta
Dec 19, 2023
k How do you make a forum
Blue_banana4   2
N Nov 6, 2023 by Blue_banana4
how do you make a forum
I would like to create a forum that allows people to be free with each other, post about things they think are important, and just generally support each other. I am wondering how one creates a forum.
2 replies
Blue_banana4
Nov 5, 2023
Blue_banana4
Nov 6, 2023
k How to scroll to bottom of topic
Crosstan81   2
N Apr 27, 2023 by Amkan2022
Is there a way to automatically go to the bottom of a topic since it's kind of annoying to have to manually scroll all the way down?
2 replies
Crosstan81
Apr 27, 2023
Amkan2022
Apr 27, 2023
k How to draw these grey lines?
PhilippineMonkey   4
N Dec 11, 2022 by s12d34
Could someone help me to draw such grey line?
4 replies
PhilippineMonkey
Dec 11, 2022
s12d34
Dec 11, 2022
k Private Forum Emptied
Mbean16   4
N Nov 20, 2022 by Sotowa
I made a private forum where I kept my solutions to writing problems from AoPS classes along with feedback and scores, mainly to notice progress and save some of my favorite solutions. I've used the forum for about 6 months, and today I noticed that all of the topics were deleted. Is there a reason for this? Is there anything I can do to reverse it?
4 replies
Mbean16
Nov 20, 2022
Sotowa
Nov 20, 2022
k New Forum?
ZoBro23   3
N Oct 31, 2022 by ZoBro23
Hi,
Is there any way I can create a new AoPS Forum? There seem to be many forums, like the Cubers Forum and the Coding Forum, so can I create a new forum? Or do I need to be an administrator to do that?

Thanks!
3 replies
ZoBro23
Oct 31, 2022
ZoBro23
Oct 31, 2022
k Re-Admin?
megahertz13   2
N Oct 19, 2022 by jlacosta
Hi AoPS Admins, in my forum
2 replies
megahertz13
Oct 19, 2022
jlacosta
Oct 19, 2022
standard Q FE
jasperE3   4
N Apr 26, 2025 by jasperE3
Source: gghx, p19004309
Find all functions $f:\mathbb Q\to\mathbb Q$ such that for any $x,y\in\mathbb Q$:
$$f(xf(x)+f(x+2y))=f(x)^2+f(y)+y.$$
4 replies
jasperE3
Apr 20, 2025
jasperE3
Apr 26, 2025
Source: gghx, p19004309
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jasperE3
11395 posts
#1
Y by
Find all functions $f:\mathbb Q\to\mathbb Q$ such that for any $x,y\in\mathbb Q$:
$$f(xf(x)+f(x+2y))=f(x)^2+f(y)+y.$$
Z K Y
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ErTeeEs06
69 posts
#2 • 1 Y
Y by jasperE3
Seems like a nice problem! This is my current progress after 30 minutes of work. To be continued... (hopefully)

Denote the given assertion by $P(x, y)$.

$P(-1, 0)$ gives $f(-1)=0$. Now comparing $P(-1, \frac{x}{2})$ and $P(0, \frac{x}{2})$ gives that $$f(f(x))=f(f(x-1))+f(0)^2$$for all $x\in \mathbb{Q}$. From simple induction it follows that $$f(f(n))=(n+1)f(0)^2+f(0)$$for all integers $n$.

$P(0, -1)$ gives $-f(0)^2+f(0)=f(0)^2-1$ and this quadratic has solutions $f(0)=1, f(0)=-\frac{1}{2}$. I'll now split into 2 cases.

Case 1: $f(0)=1$

From the things found before we know $f(f(n))=n+2$ for all integers $n$ and $P(0, n)$ yields $2n+2=1+f(n)+n$ and therefore $f(n)=n+1$ for all integers $n$.

Case 2: $f(0)=-\frac{1}{2}$

From the things found before we know $f(f(n))=\frac{n-1}{4}$ and $P(0, n)$ yields $f(n)=-\frac{n+1}{2}$ for all integers $n$.
Z K Y
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jasperE3
11395 posts
#3
Y by
bump, above poster has the right idea, one more insight is needed (if you haven't seen this idea before)
ideas from the original thread may be useful
This post has been edited 1 time. Last edited by jasperE3, Apr 22, 2025, 4:31 AM
Z K Y
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ErTeeEs06
69 posts
#4
Y by
jasperE3 wrote:
bump, above poster has the right idea, one more insight is needed (if you haven't seen this idea before)
ideas from the original thread may be useful

I tried for some more time but didn't really make progress. Only managed to find for all values of the form $\frac{n}{2^k}$ but no clue how to do it for other values. Can you give a hint?
Z K Y
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jasperE3
11395 posts
#5
Y by
ok ill post my solution
jasperE3 wrote:
Find all functions $f:\mathbb Q\to\mathbb Q$ such that for any $x,y\in\mathbb Q$:
$$f(xf(x)+f(x+2y))=f(x)^2+f(y)+y.$$

As in the $\mathbb R\to\mathbb R$ solution, we get $f\left(x+\frac12\right)=f(x)+f(0)^2-\frac12$ and $f(0)\in\left\{-\frac12,1\right\}$.

Case 1: $f(0)=1$
We have, for $x\in\mathbb Q$, $f\left(x+\frac12\right)=f(x)+\frac12$ and so $f(x+n)=f(x)+n$ for $n\in\mathbb N$ by induction.
Fix $x\in\mathbb Q$, let $n>0$ be the denominator of $x+f(x)$ in lowest terms so that $nx+nf(x)$ is an integer (existence guaranteed because $x+f(x)\in\mathbb Q$). Then using $P(x+n,y)$ and $P(x,y)$ we have:
\begin{align*}
f(x)^2+f(y)+y+nx+nf(x)+n^2+n&=f(xf(x)+f(x+2y))+nx+nf(x)+n^2+n\\
&=f(xf(x)+f(x+2y)+nx+nf(x)+n^2+n)\\
&=f((x+n)(f(x)+n)+f(x+2y)+n)\\
&=f((x+n)f(x+n)+f(x+2y+n))\\
&=f(x+n)^2+f(y)+y\\
&=f(x)^2+2nf(x)+n^2+f(y)+y
\end{align*}so simplifying we get $\boxed{f(x)=x+1}$ which satisfies the equation.

Case 2: $f(0)=-\frac12$
Similarly, we have, for $x\in\mathbb Q$, $f\left(x+\frac12\right)=f(x)-\frac14$ and so $f(x+n)=f(x)-\frac n2$ for $n\in\mathbb N$ by induction.
Fix $x\in\mathbb Q$, let $n>0$ be the denominator of $-x+2f(x)$ in lowest terms so that $-nx+2nf(x)$ is an integer (existence guaranteed because $-x+2f(x)\in\mathbb Q$). Then using $P(x+2n,y)$ and $P(x,y)$ we have:
\begin{align*}
f(x)^2+f(y)+y+\frac12nx-nf(x)+n^2+\frac12n&=f(xf(x)+f(x+2y))+\frac12nx-nf(x)+n^2+\frac12n\\
&=f(xf(x)+f(x+2y)-nx+2nf(x)-2n^2-n)\\
&=f((x+2n)(f(x)-n)+f(x+2y)-n)\\
&=f((x+2n)f(x+2n)+f(x+2y+2n))\\
&=f(x+2n)^2+f(y)+y\\
&=f(x)^2-2nf(x)+n^2+f(y)+y
\end{align*}so simplifying we get $\boxed{f(x)=\frac{-x-1}2}$ which satisfies the equation.
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