Plan ahead for the next school year. Schedule your class today!

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k a July Highlights and 2025 AoPS Online Class Information
jwelsh   0
Jul 1, 2025
We are halfway through summer, so be sure to carve out some time to keep your skills sharp and explore challenging topics at AoPS Online and our AoPS Academies (including the Virtual Campus)!

[list][*]Over 60 summer classes are starting at the Virtual Campus on July 7th - check out the math and language arts options for middle through high school levels.
[*]At AoPS Online, we have accelerated sections where you can complete a course in half the time by meeting twice/week instead of once/week, starting on July 8th:
[list][*]MATHCOUNTS/AMC 8 Basics
[*]MATHCOUNTS/AMC 8 Advanced
[*]AMC Problem Series[/list]
[*]Plus, AoPS Online has a special seminar July 14 - 17 that is outside the standard fare: Paradoxes and Infinity
[*]We are expanding our in-person AoPS Academy locations - are you looking for a strong community of problem solvers, exemplary instruction, and math and language arts options? Look to see if we have a location near you and enroll in summer camps or academic year classes today! New locations include campuses in California, Georgia, New York, Illinois, and Oregon and more coming soon![/list]

MOP (Math Olympiad Summer Program) just ended and the IMO (International Mathematical Olympiad) is right around the corner! This year’s IMO will be held in Australia, July 10th - 20th. Congratulations to all the MOP students for reaching this incredible level and best of luck to all selected to represent their countries at this year’s IMO! Did you know that, in the last 10 years, 59 USA International Math Olympiad team members have medaled and have taken over 360 AoPS Online courses. Take advantage of our Worldwide Online Olympiad Training (WOOT) courses
and train with the best! Please note that early bird pricing ends August 19th!
Are you tired of the heat and thinking about Fall? You can plan your Fall schedule now with classes at either AoPS Online, AoPS Academy Virtual Campus, or one of our AoPS Academies around the US.

Our full course list for upcoming classes is below:
All classes start 7:30pm ET/4:30pm PT unless otherwise noted.

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0 replies
jwelsh
Jul 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
Functional equation
thisisben   3
N 5 hours ago by megarnie
Determine all functions $f:\mathbb{C}\longmapsto \mathbb{C}$ satisfying $f(a+b)-f(a)=b^2$ for any $a$ and $b$.
3 replies
thisisben
Aug 21, 2012
megarnie
5 hours ago
Mathematics
Yoyotravislamar   0
5 hours ago
The question is:- for a,b,c,d>0 prove that square root of((a²+b²+c²+d²)/4) greater than or equal to cube root of((abc +abd+acd+bcd)/4). It is the question on page 179 of Arthur Engel's book problem solving strategies. What I tried was using the A.P. and G.P. relationship but then the cube root is giving problem. I then thought of first cubing both sides then squaring but then the L.H.S is coming to the power 6. Please solve it.
0 replies
Yoyotravislamar
5 hours ago
0 replies
KVS IOQM 14 square inscribed in equilateral
parmenides51   4
N 6 hours ago by SomeonecoolLovesMaths
Let $ABC$ be an equilateral triangle with side length $10$. A square $PQRS$ is inscribed in it, with $P$ on $AB, Q, R$ on $BC$ and $S$ on $AC$. If the area of the square $PQRS$ is $m +n\sqrt{k}$ where $m, n$ are integers and $k$ is a prime number then determine the value of $\sqrt{\frac{m+n}{k^2}}$.
4 replies
1 viewing
parmenides51
Jan 31, 2021
SomeonecoolLovesMaths
6 hours ago
Fractions Equal Integers
joml88   6
N Yesterday at 6:42 PM by OWOW
For how many ordered pairs of positive integers $(x,y),$ with $y<x\le 100,$ are both $\frac xy$ and $\frac{x+1}{y+1}$ integers?
6 replies
joml88
Dec 22, 2005
OWOW
Yesterday at 6:42 PM
k I've been wrongfully disabled
K124659   5
N Jul 5, 2025 by K124659
Summary of the problem: My alcumus account has been "banned"
Page URL: Anywhere on alcumus
Steps to reproduce (I reccomend you don't):
1. Answer questions extremely quickly whilst spamming the enter button
Expected behavior: You'll get banned. I believe this is some sort of system to disable bots.
Frequency: I'm not sure.
Operating system(s): Acer 311 Chromebook
Browser(s), including version: Google Chrome
Additional information: I believe this is due to the fact that I knew most of the questions either by heart or because they are extremely easy (It was multiplying fractions in pre-algebra that got me banned), and as a result I was going too fast and was spamming inputs into the system, similar to a bot. I wasn't using a bot, however. I'm not even grinding HOF- I had broken record as a quest with my problem streak being 399 previously, so my usage of the same subject to get a bunch correct was lowk necessary ngl.
5 replies
K124659
Jul 5, 2025
K124659
Jul 5, 2025
k Searching for keywords
Cats_on_a_computer   1
N Jul 4, 2025 by Demetri
Quick question because I’m new here, I keep searching keywords in the community search functions to check if they’ve been posted before, and every time it ended up not finding the original, leading to a repost. This has happened so many times I’ve decided not to post anymore until I can somehow find a way to efficiently search for it.
I accidentally reposted a Putnam 2006, even though I searched for the keywords in the question, but since I didn’t know it was a Putnam problem (I had seen it somewhere else), I didn’t manage to find the problem so unknowingly reposted it.
1 reply
Cats_on_a_computer
Jul 4, 2025
Demetri
Jul 4, 2025
k REQUEST LOCK
KangarooPrecise   25
N Jul 3, 2025 by ahxun2006
On my username, why is there 3 dots after it, when 2 letters are missing?
25 replies
1 viewing
KangarooPrecise
Jul 2, 2025
ahxun2006
Jul 3, 2025
Processing module python not working
Demetri   7
N Jul 3, 2025 by jmr2010
The following code doesn't work, because canvas isn't implemented for the processing module:
import processing
def setup():
    processing.size(200, 200)
def draw():
    processing.ellipse(100, 100, 50, 50)
    processing.noLoop()
processing.run()

I believe this is an easy fix, someone just forgot to add the line "Sk.canvas = outcanvas;"(or something similar) in the code for the pywindow, which would give an output.
7 replies
Demetri
Jul 1, 2025
jmr2010
Jul 3, 2025
k FOUR PROBLEMS
CurlyFalcon55   4
N Jul 3, 2025 by CurlyFalcon55
There are four homework problems that are REALLY BUGGING ME because I CANNOT FIND THE ANSWER. :mad:
Can I make a forum where I can ask questions about these problems? Can I make one as long as it follows the AoPS Honor Code and the Terms of Service? (I can explicitly state that in the forum.)
If I have to I can make it private with a few select people. Or can I make a blog version? ;)

I know this was kind of already adressed in the "Is there a forum?" thread, but that was for existing forums. This is for a potential new public/private forum. :)

Read before replying

IMAGE
4 replies
CurlyFalcon55
Jul 2, 2025
CurlyFalcon55
Jul 3, 2025
k help me out here guys
the_mathtrovert_next_door   1
N Jul 1, 2025 by MathDolphin95
its been 30 days since i joined, but im still not able to add my status or upload my profile picture, or use latex in the forums, this is really bugging me out
1 reply
the_mathtrovert_next_door
Jul 1, 2025
MathDolphin95
Jul 1, 2025
k Most stamina xp
DramaticPython94   9
N Jul 1, 2025 by PikaPika999
Is there a limit to the stamina XP you can get in one week? I have 4200 XP this week, but I can't find any more problems with stamina XP. On the HoF leaderboard, only littleduckysteve has more than 4200 XP.
9 replies
DramaticPython94
Jun 26, 2025
PikaPika999
Jul 1, 2025
k Refreshing a user's post takes you from user posts list to forum
V0305   6
N Jun 30, 2025 by jlacosta
Summary of the problem Going to the list of a user's posts, opening a post, then refreshing the page opens the forum the post is in, rather than reopening the list of the user's posts. (Intended feature?)
Page url See steps below
Steps to reproduce
1. Go to any AoPS user's webpage, such as https://artofproblemsolving.com/community/user/588328 (which is me).
2. In the box titled Activity, click "Click to view posts".
3. A list of posts should appear. Click any one of the posts.
4. The post should now take up most of the horizontal space of the page, but the list of posts should still be visible and scrollable on the left side (assuming the device's screen is wide enough).
5. Refresh the page.
6. (bug?) Now, the forum the post is in will appear, and the scrollable list of posts is now posts of the forum (assuming the device's screen is wide enough), not of the user. Basically, refreshing the page takes you to a different page. The webpage's url also changes.
Expected behavior The list of posts and the opened post should reappear - refreshing the page shouldn't change the page's contents.
Frequency Always
Operating systems macOS Sequoia 15.5, iPadOS 18.5, iOS 18.5 (I tested the bug on a Mac, an iPad, and an iPhone)
Browsers Firefox 140.0.2 on the Mac, DuckDuckGo 7.174.1.0 on the iPad and iPhone
Additional information I discovered this bug when I accidentally pressed Command + R on a user's post page (like the page you would be on after step 3). Also, there seems to be nothing wrong (no error messages) in the console. Also, interestingly refreshing causes the bug, rather than fixing the bug (or in that case, a glitch).
6 replies
V0305
Jun 30, 2025
jlacosta
Jun 30, 2025
Cannot post PHP
char0221   5
N Jun 30, 2025 by CurlyFalcon55
Summary of the problem: If I try to post anything with PHP (a coding language), it
Page URL: In any forum or private messages
Steps to reproduce:
1. Create a post.
2. Put some PHP inside, can't give example
Expected behavior: Should post the message
Frequency: 100%
Operating system(s): macOS Sequoia 15.2.1
Browser(s), including version: Safari
Additional information: See attachments
5 replies
char0221
Apr 30, 2025
CurlyFalcon55
Jun 30, 2025
k Adops alcumus quest Jack of all trades
anstar   24
N Jun 30, 2025 by CurlyFalcon55
The "Jack of all trades" says 5 alcumus subject while there are 6 now. The recent additionn of intermeadiate algebra is the probably the cause :oops_sign:
24 replies
anstar
Nov 29, 2018
CurlyFalcon55
Jun 30, 2025
Greatest Integer function and Fractional Part Function
P162008   3
N Jun 7, 2025 by sl1345961
P1. Find the value of $S$ defined as ($\lfloor . \rfloor$ denotes greatest integer function, $\{.\}$ denotes the fractional part function)

$S = \sum_{k=1}^{7} \sum_{r=k^2 + 1}^{k^2 + 2k} \left\lfloor \frac{1}{\{\sqrt{r}\}} \right\rfloor.$

P2. Prove that $\sum_{r=0}^{n-1} \left\lfloor \frac{n + 2^r}{2^{r + 1}} \right\rfloor = n \forall n \in N.$

P3. Find $\lambda = \left\lfloor \sum_{r=1}^{200} (\sqrt{100^2 + r}) \right\rfloor.$

P4. Find $\lambda = \sum_{k=1}^{7} \sum_{r=1}^{2k}\left\lfloor \frac{2k}{r} \right\rfloor.$
3 replies
P162008
Jun 7, 2025
sl1345961
Jun 7, 2025
Greatest Integer function and Fractional Part Function
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P162008
250 posts
#1
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P1. Find the value of $S$ defined as ($\lfloor . \rfloor$ denotes greatest integer function, $\{.\}$ denotes the fractional part function)

$S = \sum_{k=1}^{7} \sum_{r=k^2 + 1}^{k^2 + 2k} \left\lfloor \frac{1}{\{\sqrt{r}\}} \right\rfloor.$

P2. Prove that $\sum_{r=0}^{n-1} \left\lfloor \frac{n + 2^r}{2^{r + 1}} \right\rfloor = n \forall n \in N.$

P3. Find $\lambda = \left\lfloor \sum_{r=1}^{200} (\sqrt{100^2 + r}) \right\rfloor.$

P4. Find $\lambda = \sum_{k=1}^{7} \sum_{r=1}^{2k}\left\lfloor \frac{2k}{r} \right\rfloor.$
This post has been edited 5 times. Last edited by P162008, Jun 8, 2025, 12:57 AM
Reason: Typo
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trangbui
819 posts
#2
Y by
The final answer is \(\boxed{0}\).
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pingpongmerrily
4004 posts
#3
Y by
I'm pretty sure that the minimum value of $r$ is $2$, then every term in the summation will be $0$, so the answer is just $0$.
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sl1345961
31 posts
#4
Y by
P162008 wrote:
P1. Find the value of $S$ defined as ($\lfloor . \rfloor$ denotes greatest integer function, $\{.\}$ denotes the fractional part function)

$S = \sum_{k=1}^{7} \sum_{r=k^2 + 1}^{k^2 + 2k} \lfloor \frac{1}{\{\sqrt{r}\}} \rfloor.$

P2. Prove that $\sum_{r=0}^{n-1} \lfloor \frac{n + 2^r}{2^{r + 1}} \rfloor = n \forall n \in N.$

P3. Find $\lambda = \lfloor \sum_{r=1}^{200} (\sqrt{100^2 + r}) \rfloor.$

P4. Find $\lambda = \sum_{k=1}^{7} \sum_{r=1}^{2k}\lfloor \frac{2k}{r} \rfloor.$
I'll do num 2, which I believe has a typo. The correct sum should be $\sum_{r=0}^{\infty} \left\lfloor \frac{n+2^r}{2^{r+1}} \right\rfloor.$

I will prove that this is equal to $n.$

Claim: $\lfloor x \rfloor + \left\lfloor x+\frac{1}{2} \right\rfloor = \lfloor 2x \rfloor.$
We will do casework on $\{ x \}.$ Suppose $x = I + f,$ where $0\leq f < \frac{1}{2}.$ Then $LHS = I + I = 2I,$ and $RHS = 2I.$ Now suppose $\frac{1}{2} \leq f < 1.$ Then we have $LHS = I + (I + 1).$ Note that $2x = 2I + 2f$ and $2I + 1\leq 2I + 2f < 2I + 2$ by our established inequalities. Thus, $\lfloor 2x \rfloor = 2I + 1.$ Thus in all cases of $f$ our assumption holds, and it is thus true.

Going back to the problem, notice that
$$\sum_{r=0}^{\infty} \left\lfloor \frac{n+2^r}{2^{r+1}} \right\rfloor = \sum_{r=0}^{\infty} \left\lfloor \frac{n}{2^{k+1}} + \frac{1}{2} \right\rfloor.$$Rearranging our claim, we have that $\lfloor 2x \rfloor - \lfloor x \rfloor = \left\lfloor x + \frac{1}{2}  \right\rfloor.$ Thus
$$ \sum_{r=0}^{\infty} \left\lfloor \frac{n}{2^{k+1}} + \frac{1}{2} \right\rfloor =  \sum_{r=0}^{\infty} \left(\left\lfloor \frac{n}{2^k}\right\rfloor - \left\lfloor \frac{n}{2^{k+1}}\right\rfloor\right).$$All terms in the sum collapse except for the first term. The first term is simply $\left\lfloor \frac{n}{2^0} \right\rfloor = n,$ and thus we have proven this sum is equal to $n.$
This post has been edited 1 time. Last edited by sl1345961, Jun 7, 2025, 11:59 PM
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